First order Definition and 585 Threads

In mathematics and other formal sciences, first-order or first order most often means either:

"linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or
"without self-reference", as in first-order logic and other logic uses, where it is contrasted with "allowing some self-reference" (higher-order logic)In detail, it may refer to:

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  1. U

    How can a first order nonlinear differential equation be solved?

    Hello: I discovered this forum while looking for advice on solving a first order nonlinear differential equation. The equation I am trying to solve is dy/dx=(3ay+3bx^2y^2)/(3x-bx^3y) a and b are constants. The equation is not exact, nor is it homogeneous. I have failed to separate the...
  2. L

    What is the approach for solving a first order Riccati differential equation?

    Homework Statement For the d.e y' = x^2+y^2 Show that the solution with y(0)=0 has a vertical asymptote at some point x_0, Then I have to try and find the upper and lower bounds for x_0 I'm not able to solve this for y because when I bring the y^2 to the LHS The Attempt at a...
  3. S

    Stark Effect using first order variation theory.

    EDIT: Sorry... I have to use perturbation theory. My mistake. Hey... I have a quick question. I have to calculate the approximate change in energy via variation theory when the 'error' Hamiltonian for the Stark effect is defined as: |\vec{E}|cos\theta\bullet eR If I'm not mistaken, the change...
  4. A

    Engineering Solving First Order Circuits Homework

    Homework Statement Ok, let's say I have a first order circuit with i_s = Acos(wt+phase) (like in the pic). I'm having problem with the private solution, let's say I pick my private solution like this: i_p = Bcos(wt + phase) = Ccos(wt) + Dsin(wt) (right?) After I place this i_p in the...
  5. A

    Engineering Solving 1st Order Circuits: Private Solution & Finding C, D

    Ok, let's say I have a first order circuit with i_s = Acos(wt+phase) (like in the pic). I'm having problem with the private solution, let's say I pick my private solution like this: i_p = Bcos(wt + phase) = Ccos(wt) + Dsin(wt) (right?) After I place this i_p in the equation I come up with...
  6. K

    Integrating the first order rate law

    -d[A]/dt = k[A] - Int( d[A]/[A]) = Int (k dt) - ( ln[A] + ln[A0] ) = kt ln[A] = -kt - ln[A0] Where am I wrong?
  7. M

    Can a Nonlinear DE with Constant Coefficients be Solved Analytically?

    dear friends, i need to solve analitically(also by means of approximate methods) the following nonlinear differential equation: (A+BTs^(3))*dTs/dt+C*Ts^(4)=D where Ts is a function of t. A, B, C and D are costants. the initial condition is Ts(0)=Ti. I would be so grateful if anyone can...
  8. F

    First Order DE problem (electric circuit)

    (dq/dt) + (5/(20+t))q = 20/(20+t) ... t=0 , q=1 (a) Find the charge on the capacitor at any time. This is linear so i found the integrating factor which is (20+t)^5 and solved q(20+t)^5 = 20 integral ((20+t)^4) dt and got q(20+t)^5 = 4((20+t)^5) + C my C value i got was...
  9. R

    First order differential equation help

    I have a problem solving a first order differential equation: dT/dP - C2/T = C1 Where C2 and C1 are just constants, the differential equations book I have does not address the situation of 1/T. I am trying to develop my own integrating factor but it would be nice for a little guidance.
  10. U

    Can You Solve This System of First Order PDEs in Game Theory?

    Hello, I have been struggling at solving what I think is a system of 1st order PDEs. Here is what I have: \frac{dy1}{dt1} = y1*F1(t1,t2) + F2(t1,t2) \frac{dy2}{dt2} = y2*F1(t2,t1) + F2(t2,t1) These equations have been obtained after modeling a problem using the game theory. More...
  11. T

    Transform to system of first order equations

    Homework Statement u'''-8u''+2u'-3u=0 Homework Equations The Attempt at a Solution So I let: x1 = u then x1' = u' x2 = u' then x1' = x2 and x2' = u'' x3 = u'' then x2' = x3 and x3' = u''' I have only done these problems with second order equations, so I don't understand...
  12. M

    Are the solutions to first order ODE's the same or different for x=a?

    Let be the first order ODE's y'(x)g(x)=0 and y'(x)g(x)=\delta (x-a) except when x=a the two equations are equal , however the solutions are very different y(x)=C and y(x)= C+ \int dx \frac{\delta (x-a)}{g(x)} or using the properties of Dirac delta y(x)=C+\frac{1}{g(a)}...
  13. H

    Probability in first order time-dependent perturbation theory

    Hi , Can anybody help me to solve this question? A time varying Hamiltonian H(t) induces transitions from state |k> at time t=0 to a state |j> at time t=t' with probability P(k to j(t')). Use first order time-dependent peturbation theory to show that if P(j to k(t')) is the prababilty that...
  14. P

    Integral of first order (first kind) bessel function

    hello, while working on a problem i encountered the following integral :(limits are zero and infinity) Integral[J1(kR)dk] J1 is the first order bessel function..cudnt put 1 in subscripts.. Is there an analytical solution for this?? also is it possible to integrate it numerically...
  15. A

    First Order Diff. Eqn w/ Inital Value

    Homework Statement dy/dt = ty(4-y)/3 y(0) = y_o Suppose y_o = 0.5. Find the time T at which the solution first reaches the value 3.98 Homework Equations I separated, integrated and solved, so do i just plug in y_o wherever i see y and 0 for t to find the constant C and plug this...
  16. R

    Linear first order differential equation

    Homework Statement \frac{dy}{dx} = \frac{x^2}{2} + \frac{xy}{2} + \frac{3y^2}{2} + \frac{3y}{2} Homework Equations The Attempt at a Solution Don't really know were to begin. If anyone could tell me which method to use that would be great. I can't think of any way to solve this.
  17. F

    Linear (I think?) First Order Diff EQ

    So this equation came up: xy' + y = cos x Now I was just wondering how to solve this, all I've learned how to do is separation of variables, which cannot be used in this case. Basically I ask this because a solution for y is an infinite series, so basically I'm just wondering if the...
  18. S

    Matlalb problem with two first order ODEs

    Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...
  19. S

    MATLAB Plotting Two First Order ODEs and Two Second Order ODEs

    Homework Statement I have two questions: 1) If i have two first order ODE y(1) and y(2) (in terms of time), i know how to plot y(1) versus time and y(2) versus time but i don't know how to plot y(2) versus y(1) 2)I have two second order ODES X''=... and Z''=... to solve this, we make the...
  20. N

    Seperation of variables - first order PDE

    [SOLVED] Seperation of variables - first order PDE Homework Statement I have the expression X'(x)/X(x) = cx. How do I separate the variables? It's the fraction on the left side that annoys me. I know that X'(x) = d(X(x))/dx, but I can't use this here? EDIT: Sorry for the mis-spelled title...
  21. J

    Deduction theorem for first order logic

    If I have P l- Q in FOL and P is closed, can I infer l- P -> Q. IIRC, this is valid as long as P is closed, but my memory is a little hazy. Is that how it works?
  22. K

    How do you solve this nonlinear first order DE

    I am having trouble solving the following nonlinear first order differential equation: dy/dx = mx + b - k*y^2 The variables m, b and k are constants. I have had DE in school, but it was mostly linear first order, so I am not sure how to solve this one. Someone has recommended...
  23. B

    System of coupled first order PDE

    Hello everybody, I have a problem here related to QFT in a research project. I end up with some Dirac equation with space-time dependent mass in 2 spatial dimensions. More mathematically, the PDE to solve is \left( {i\left( {\sigma ^i \otimes I_2 } \right)\partial _i + g_y \varphi...
  24. S

    Help with first order, Bernoulli ODE

    Help with first order, "Bernoulli" ODE We just covered: -First order linear ordinary differential equations -Bernoulli Equations -Simple substitutions. This problem was assigned. Its supposedly a Bernoulli equation with respect to y, but I can't figure it out...
  25. A

    First order separable differential equation

    Homework Statement \frac{dy}{dx} + x^{2} = x Homework Equations Above. The Attempt at a SolutionAfter rearranging, I am stuck at \int \frac{1}{x-x^{2}} dx = \int dt I can't think of any u-substitution, or any other trick for integrals I could use to solve this.
  26. M

    First Order Linear Differential Equations

    Homework Statement In a particular cosmological model, the Friedmann equation takes the form L^2 (a')2 = a^2 − 2a^2 + 1, where L is a positive constant, the dot denotes time differentiation, and the initial condition is a(0) = 1. What are the units of L? Show, without solving this...
  27. N

    Solving a Nasty First Order ODE

    Homework Statement This problem is from Blanchard "Differential Equations" Chapter one review, question 32. {\frac {d}{dt}}y \left( t \right) -{\frac {y \left( t \right) {t}^{3}} {1+{t}^{4}}}=2 The Attempt at a Solution Using an integrating factor yields: {\frac {d}{dt}}...
  28. M

    First Order Differential Equations

    Homework Statement Solve the following differential equation: y' = (y/x) + (2x^3Cos(x^2)/y). Homework Equations The Attempt at a Solution You certainly can't separate variables here and you can't put it in the form in which you can find the integrating factor. This is not a...
  29. C

    Mixing Problem - Linear First Order ODE

    [SOLVED] Mixing Problem - Linear First Order ODE Homework Statement A 500-gallon tank initially contains 50 gallons of brine solution in which 28 pounds of salt have been dissolved. Beginning at time zero, brine containing 2 pounds of salt per gallon is added at the rate of 3 gallons per...
  30. K

    First order linear differential equation

    1) Solve y' + (1/t) y = t^3. Integrating factor =exp ∫(1/t)dt =exp (ln|t| + k) =exp (ln|t|) (take constant of integration k=0) =|t| ... and then I've found that the gerenal solution is: y = 1/|t| + [c + ∫(from 0 to t) |s| s^3 ds] Is this the correct final answer and is there any way...
  31. J

    Understanding First Order Logic for "Two Purple Mushrooms

    hi, could someone explain to me why the sentence - There are exactly two purple mushrooms is represented in FOL like this: (Ex)(Ey) mushroom(x) ^ purple(x) ^ mushroom(y) ^ purple(y) ^ ~(x=y) ^ (Az) (mushroom(z) ^ purple(z)) => ((x=z) v (y=z)) especially the last part i have problem with...
  32. D

    Zero and first order Hankel Transforms

    Hello everyone, I am dealing with the following problem. Solving and kinetic equation I came up with the expression H_1^(-1)[H_0(P(r))/q] where H_0 is the zero order Hankel transform, H_1^(-1) is the first order inverse Hankel transform P(r) is a function that depends on the radial...
  33. Q

    Why Does the First Order Term in QED Scattering Matrix Give No Contribution?

    Can some explain me why first order term in perturbation expansion of scattering matrix gives no contribution for every possible IN and OUT states? It is said that this is connected with the fact that condition of energy-momentum conservation cannot be satisfied for real photons and electrons...
  34. E

    First order differential equation problem.

    Homework Statement Find the general solution of 2y(x^3+1)dy + 3x^2(1-y^2)dx = 0 Homework Equations The Attempt at a Solution So I first grouped the terms with dy or dx 2y/(1-y^2) dy = -3x^2/(x^3 +1) dx after integrating both sides and solving, I got ln (1-y^2)=...
  35. I

    Translating into first order predicate expressions

    Homework Statement I have been given the following predicates of the domain of real numbers Homework Equations P(x): x>0 E(x): x is even D(x): x is exactly divisable by 5 (i) At least one integer is even (ii) There exists a positive integer that is even (iii) If x is...
  36. J

    Trouble with first order system

    Im going over some class notes on LTI systems, and attempted a problem involving first order systems. I have attached the problem, it is on page 1B.2 of the attached pdf (its in italics) Also, I have attached a word doc showing my hand working many thanks in advance
  37. R

    Solve First Order ODE: x^2yy' = (y^2-1)^(3/2)

    Homework Statement Find all solutions x^{2} y y\prime = (y^{2} - 1)^{\frac{3}{2}} Homework Equations The Attempt at a Solution I know I have to use separation of variables because it isn't linear. so I get \frac{ydy}{(y^{2} - 1)^{\frac{3}{2}}} = \frac{1}{dxx^{2}}...
  38. R

    What is the General Solution to a First Order Linear Differential Equation?

    Homework Statement Find the General Solution: xy\prime + (\ln{x})y = 0 Homework Equations The Attempt at a Solution so I used the separation of variable method to get \frac{y\prime}{y} = -\frac{\ln{x}}{x} Then I took the integral of both side to get \ln{y} =...
  39. M

    What is the graviton propagator in the first order formalism?

    With the help of harmonic gauge condition, graviton propagator can be obtained by weak field expansion around the flat Minkowski metric (assuming cosmological constant is zero). Gravitation theory can also be written in the first order (Palatini) formalism. In stead of the metric, the basic...
  40. T

    Differential Equations - First Order Systems

    Solve: dx / dt = 3*x + y dy / dt = -y As for solving this, here is what I've got so far: Since dy/dt is separable, I found that dy / y = -dt, integrated, and solved explicitly for y: y = Ce^-t I then plugged Ce^-t for y in the dx / dt portion of the system and found that...
  41. maverick280857

    Solution of First Order DE using Integrating Factors

    Hello everyone I'm stuck with a problem from Simmons (not HW). The problem asks to solve the following equation by finding an integrating factor (xy-1)dx + (x^2 - xy)dy = 0 I found by hit and trial that there can be no integrating factor that is a function of x alone or y alone. So how...
  42. O

    Where ı can find problems about first order diff. equations

    Hi. Do you know any sources where I can find good problems about first order differential equations? Thanks...
  43. L

    Solving First Order Equations: Integral Factor and Exact Differential Equation

    I have the following equation: (x^2-y^2-y)dx-(x^2-y^2-x)dy=0 I was trying to find the integral factor of this to make it a exact differential equation, but ended in a almost imposible integral. do anyone have any idea of how to make this?
  44. RadiationX

    Engineering How to Solve a First Order Transient Circuit Using Differential Equations?

    I'm having serious trouble understanding how to solve this problem using the differential equation method ( I MUST use this method). I provided the answer but my solution attempts are not producing the same result. Here is the problem...
  45. RadiationX

    Analyzing First Order Transient Circuits Using Differential Equations

    Please click the image to make it larger: http://img360.imageshack.us/img360/2049/82009866sy5.th.jpg To solve this circuit I'm going to use the differential equation approach. I'm concerned with the voltage across the capacitor at V_c(0^-) and V_c(0^+) At position 1 before the switch...
  46. RadiationX

    Engineering Differential Equation Approach to solving First Order Circuits

    We are doing transient circuit analysis in one of my engineering courses. There are two ways of solving these types of circuits: 1. The step by step approach 2. The differential equation approach. The step by step method is well documented in our textbook, but the differential equation...
  47. 0

    How Does a Magnetic Field Affect Energy Levels in a Diatomic Molecule?

    Homework Statement A diatomic molecule in a uiform magnetic field along z-axis B =(0,0,B). SO the Hamiltonian is H = \frac{\hat{l^2}}{2I} - \mu(\hat{B}\bullet\hat{i}) \mu is some co-efficient. Considering he hamiltonian above as perturbation and using first order perturbation theory find an...
  48. R

    How Do You Solve the Differential Equation kxy = (y+dx)(x+dy)?

    I have run into this problem solving differential equations of this type (they occur often doing momentum problems): kxy = (y+dx)(x+dy) where k is constant. I multiply it out to : kxy= xy + xdx + ydy + dydx Regroup and : [tex] \int {kxy} = \int {xdx} + \int {ydy} + \int {dydx} [/itex]...
  49. B

    First Order Differential Equations

    Homework Statement Solve the following differential equation using separation of variables (1+x)^2 y' = (1-y)^2 , y(1) = 2 Homework Equations The Attempt at a Solution haven't gotten very far in this at all :/ i've tried dividing both sides by (1+x)^2, in order to get y' on it's own...
  50. S

    First order ODE initial value problem

    Homework Statement Given the below stated equations I need to find the exact polynomial given the initial condition. y(0) = 1 y = 4*t*sqrt(y) Homework EquationsThe Attempt at a Solution I simply disregard the initial value condition and get y = t^4 How can I find the fourth order...
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