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. T

    Solve first order difference equation

    Homework Statement Solve the first order difference equation. Homework Equations x[n] - x[n-1] = n(n+1)/2 x[1] = 1 The Attempt at a Solution Homogenous solution: Characteristic equation: r - 1 = 0 <=> r = 1 => yhn = C * 1^n = C Particular solution: ypn = ? I'm supposed to...
  2. C

    Systems of First Order Linear Equations

    Homework Statement Systems of first order equations can sometimes be transformed into a single equation of higher order. Consider the system (1) x1' = -2x1 + x2 (2) x2' = x1 - 2x2 Solve the first equation for x2 and substitute into the second equation, thereby obtaining a second order...
  3. B

    Systems of first order linear equations involving wronskian and matrices

    Homework Statement If y3(0) = 2y2(0) - y1(0), what is W(3)? Homework Equations \frac{d}{dt} y(t) = A(t) y(t), A(t) = [1 et e-t] [e-t 0 et] [2 sin(t) -1] The Attempt at a Solution I...
  4. N

    Why does Lagrangian in QFT only include first order derivative of field?

    Please teach me this: Why the Lagrangian in QFT does not include high order derivative of field?Is it correct the reason being all fields obey the only Dirac and Klein-Gordon equations? Thank you very much for your kind helping.
  5. K

    System of Two Dimensional First Order ODE

    Homework Statement Find all solutions to [dx/dt; dy/dt] = [1, 2; 0, 1]*[x; y] Homework Equations the eigenvalue characteristic equation: det(A-λ*I)=0 The Attempt at a Solution This results in real, repeated eigen values: λ1,2 = 1 for λ1 = 1, (1-1)k1 + 2k2 = 0 choose k1 =...
  6. E

    How can I solve this first order DE with initial value y(0)=3^(1/2)/2?

    The problem: dx(1-y^2)^1/2=dy(1-x^2)^1/2 y(0)=3^(1/2)/2 My attempt: I separated the variables and integrated, and came up with sin^-1(x)+c=sin^-1(y) This is where i am stuck. any suggestions? did I run astray anywhere?
  7. X

    First order differential equation

    I am asked to find the general solution to: \dfrac{dy}{dx}\sin x + y \sec x = \cos^2 x I don't quite know where I am going with this one; by simply looking at it, I can't seem to see what I would differentiate in order to get the left side and equally, I don't know if dividing through by...
  8. N

    How to solve this First Order Differential Equation?

    How to solve this differential equation? dy/dx = - (3yx^(2) + y^(2)) / (2x^(3) + 3xy) I've tried finding an integrating factor in order to make it exact, but I don't know what to do with this. The answer is given as x^(3)y^(2) + xy^(3) = c I'm so confused. I separated it...
  9. P

    First order nonlinear differential equation

    Homework Statement Find the orthogonal trajectories of the given families of curves. x^2 + y^2+2Cy=1 Homework Equations The book has covered homogeneous and separable methods.The Attempt at a Solution To find the orthogonal trajectories, we simply find the curves whose tangents are...
  10. K

    When Will the Alarm Sound for a First Order Transfer Function?

    Homework Statement The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order transfer function (in deviation variables) that relates the measured value Pm to the actual pressure, P: Pm'(s)/P'(s)=1/(30s+1). Both Pm' and P' have units of psi and the time constant...
  11. N

    Solve 1st Order ODE: x^2+y^2+2xy+y^2+(x^3/3)dy/dx=0

    i have this differential equation of the first order [x^2+y^2]+[2xy+y^2+(x^3/3)]dy/dx=0 i tried to solve it by substitution putting x^2+y^2=v ,but it doesn't work also it is not exact or homogeneus to solve it by these methods. I still believe it can be solved using substitution but i can't...
  12. fluidistic

    Transforming a Non-Linear DE into Bernoulli's Form

    Homework Statement Solve the following DE: 2xyy'=4x^2+3y^2. Homework Equations Bernoulli's DE: y'+P(x)y=Q(x)y^2. The Attempt at a Solution I know that the original DE isn't under Bernoulli's form, but I have thought a lot on the problem and my feeling is that if I could find a...
  13. fluidistic

    Non linear, non exact first order DE

    Homework Statement I must solve the following DE: x+y+1+(2x+2y-1)y'=0. I can't write the DE under the form y'+P(x)y=Q(x) so I can't use the integrating factor method. I checked out of the DE is exact, and it's not.Homework Equations Not really sure.The Attempt at a Solution I tried a...
  14. S

    Special case of nonlinear first order ordinary differential equation.

    Hi there, I've having problems solving a particular nonlinear ODE. Any help/suggestions will be highly appreciated. The nonlinear ODE is: v[t]*v'[t] + (4*v[t])/(t^2 - 1) = t/(t^2 - 1) Thank you.
  15. G

    Integrating factor for first order linear equations uniqueness theorem

    My book stated the following theorem: If the functions P(x) and Q(x) are continuous on the open interval I containing the point x0, then the initial value problem dy/dx + P(x)y = Q(x), y(x0)=y0 has a unique solution y(x) on I, given by the formula y=1/I(x)\intI(x)Q(x)dx where I(x) is the...
  16. S

    Solve 1st Order ODE: xyy'=x^2+3y^2, y(1)=2

    Homework Statement Find the following IVP Diff.Eq. xyy'=x^2+3y^2 y(1)=2 Homework Equations The Attempt at a Solution I've been struggling with this problem for a while now. I believe I have figured out it is homogenous, thus y=ux substitution applies. Through some work I have arrived at...
  17. A

    Are We Missing Solutions in First Order Non-linear PDEs?

    Let us consider the following partial differential equation: {(}\frac{\partial z}{\partial x}{)}^2{+}{(}\frac{\partial z}{\partial y}{)}^{2}{=}{1} ---------- (1) The general solution[you will find in the texts: http://eqworld.ipmnet.ru/en/solutions/fpde/fpde3201.pdf is given by...
  18. T

    How Is Equilibrium Price Stability Determined in Market Dynamics?

    Homework Statement In the market for a certain good, the price p(t) adjusts continuously in the presence of excess supply or demand: \frac{dp}{dt} = F(D(p)-S(p)) where F(0) = 0, F'>0. Obtain the condition for stability of the equilibrium price p* in terms of the slopes D'(p*) and S'(p*), and...
  19. A

    First order coherence classical optics problem

    Homework Statement Hi, I am trying to work through exercise 2.1 on page 37 of Microcavities (by alexy kavokin, jeremy baumberg, guillaume malpuech and fabrice laussy) the problem is to prove | g^{(1)}(\tau) | = | cos( \frac{1}{2}(\omega_1 - \omega_2)\tau) ) | where...
  20. P

    First order nonlinear differential equation Help needed.

    Hi All, I have been trying to solve following nonlinear differential equation, but I couldn't solve it. 0 = a*[f(t)]^{z/(z-1)} + (-t+C)*f(t) + b*[df(t)/dt] where a, b and C are constants and 0< z<1. Could you please help me how to solve this nonlinear differential equation? I would...
  21. D

    Partial differential equation help needed (first order)

    Homework Statement Let u be a solution of a(x,y)u_{x}+b(x,y)u_{y}=-u (I) of class C^{1} in the closed unit disk \Omega in the xy-plane. Let a(x,y)x+b(x,y)y>0 (II) on the boundary of \Omega. Prove that u vanishes identically. (Hint: Show that on \Omega max u\leq 0, min u \geq 0, using conditions...
  22. T

    Break Second order ODE into a system of first order ODE's

    Homework Statement I haven't done this for several years and have forgotten. Kicking myself now over it since it looks like something so simple but i cannot figure it out... I need to break this second order ODE into a system of first order ODE's in matrix form to use within a crank...
  23. C

    First order linear PDE, understanding solution/method

    Homework Statement Solve the initial boundary value problem: u_t + cu_x = -ku u is a function of x,t u(x,0) = 0, x > 0 u(0,t) = g(t), t > 0 treat the domains x > ct and x < ct differently in this problem. the boundary condition affects the solution in the region x < ct, while...
  24. M

    How Do You Solve This First Order ODE with Given Condition?

    The question is x^2dy/dx + y^2=0 , y(1)=3 I re-arrange the equation to get -1/y^2dy=1/x^2dx Seperated them, then I integrate both sides to get 1/y=-1/x + c Now I don't get how they got the answer y=3x/(4x-3), as when I try use the condition I get a different answer, could anyone help? I...
  25. B

    First Order Notch Filter: Building Guide

    Hello. Is there any way to build a band reject filter ('notch') whose transfer function, H(s), has only two complex zeros and only one real pole? For example: H(s) = \displaystyle\frac{s^2+4}{s+1000}
  26. D

    How many B.C. are necessary for first order PDE set?

    Hi I have a set of two linearized integro-partial-differential equations with derivatives of first order (also inside the integrals). How many boundary (initial) conditions should I give for such problem for the solution to be unique? is the 'initial condition that intersect once with the...
  27. estro

    Non-linear first order ODE: Solving with Exact Form

    I'm trying to solve the following ODE: ydx+(\frac {e^x}{y}-1)dy=0 I tried to transfer this ODE into exact form but no luck. Will appreciate any help.
  28. Y

    First Order System's Time Constant

    Hello, I have a question on a the units of a first order system's time constant. If i have a first order system the basic transfer function will be: K/(tau*s+1) where K is the Gain, and tau is the system's time constant. tau's units, according to what I've learned, are [sec]. but...
  29. H

    What is the 'first order' diffraction peak?

    Could someone explain what the 'first order' diffraction peak is?
  30. J

    How to prove: Uniqueness of solution to first order autonomous ODE

    Hello! I would like to prove the following statement: Assume f\in C^{1}(\mathbb{R}). Then the initial value problem \dot{x} = f(x),\quad x(0) = x_{0} has a unique solution, on any interval on which a solution may be defined. I haven't been able to come up with a proof myself, but would...
  31. A

    Solve the first order hyperbolic equation

    Solve the first order hyperbolic equation 3 du/dx + 2x du/dt =2u With initial condition: u(x,0) = 2x+4 My attempt at a solution I usually adopt the method of characteristics: dx/a = dt/b = du/c So from the above: a=3, b=2x and c=2u am I on the right track here?
  32. M

    Solving a First Order Linear ODE System with a Constraint

    Hello all, I don't have much experience with ODEs. I have a simple system, which I believe is first order linear, similar to the following: dA/dt = 2A + 3B - C dB/dt = A + 2B - C dC/dt = -2A + 5B - 2C Now I would like to include the constraint that A + B + C = 1. How do I do this...
  33. S

    Can the Separable First Order ODE be solved with a different answer?

    2r(s^2+1)dr + (r^4 + 1)ds = 0 2.book answer different than mine...book's answer: r^2 + s = c(1 -r^2 s) 3. 2r(s^2+1)dr =- (r^4 + 1)ds -2r/r^4+1 dr = 1/s^2+1 ds int -2r/r^4+1 dr = int 1/s^2+1 ds with u substitution on left we have u = -2r, etc. tan^-1 r^2 = - tan^ -1 s + c tan^-1 r^2 +...
  34. K

    First order ordinary differential equation

    Homework Statement I haven't done ODEs in a few years and I am trying to do this equation: m_{Hg}C_{p,Hg}\frac{dT_{Hg}}{dt} = Q Q = hA(T_{air} - T_{Hg}) T_{Hg}(t = 0) = 20 I need to find T_{Hg}(t=590) Homework Equations The Attempt at a Solution h, A, m_{Hg}, C_{p,Hg}...
  35. B

    Engineering First order circuit with DC sources

    The circuit is in the attachment, plus the values that I've managed to find out so far. Im having problem with figuring out the voltage at t=infinity. So far i know that when t->infinity that inductors become short circuit. It says to apply current division and then Ohm's Law as a hint, and...
  36. Y

    General Solution of the first order differential equation

    dy/dt + y = \infty \sumSin(nt)/n^2 n=1 Ok still a bit new with all these symbols and stuff but that is the basic jist of it. y(t) = yh(t) + yp(t) it what i thought about using to start off with, yh(t) = Acos2t + Bsin2t. Then subbing yp(t) into the differential equation. Not really...
  37. Y

    General Solution of the first order differential equation

    dy/dt + y =\infty\sumn=1Sin(nt)/n^2
  38. Y

    General Solution of the first order differential equation

    dy/dt + y = Sigma Sin(nt)/n^2
  39. L

    Calculating First Order Photon Self-Energy Integral

    Hi, I am trying to calculate the first order photon self-energy. At a point, I must calculte the following integral : \int d^4k \frac{(k+q)^\mu k^\nu+(k+q)^\nu k^\mu - g^{\mu \nu}(k \cdot(k+q) - m^2}{k^2 + 2x(q\cdot k) + xq^2 -m^2} I know that I must wick rotate and that k^2 will...
  40. S

    Substitution Methods for first order differential equations

    I have the following equation:: xy' = y + 2*sqrt(xy) I know I should either use the F(y/x) substitute or Bernoulli's method of substitution but I'm not sure how to manipulate the equation to determine which it is. If someone had some helpful tips on how to start, please let me know...
  41. J

    Help: unit-step response of a first order system

    Homework Statement A first-order system G(s)=\frac{k}{s+a} and its response to a unit step input are shown in the figure below. Determine the system parameters a and K 2. The attempt at a solution I’ve tried to find K & a using MATLAB and read a lot but didn’t find...
  42. E

    Engineering Understanding First Order Circuits: DC vs. AC

    Hi, I'm confused with the solution given for this practice problem. All of these components are said to be in parallel, yet the current is worked out only across the resistors. I thought the inductor would be a short circuit to DC. Am I looking at this backwards, is it modelling the inductor...
  43. N

    How do you use the Quadratic Formula to solve First Order ODE?

    Homework Statement How do you use the Quadratic Formula to solve First Order ODE? For example, I am given this integration (see attachment at the bottom). Homework Equations The Attempt at a Solution I integrated both sides but I do not know where to go from there (see attachment at the...
  44. C

    First order differential equation transforms

    I am to find a general solution of the system of problems below. I have done so for x(t) but am unsure how to find it for y(t)... x'=y, y'=-x x''=y=-x x''+x=0 Characteristic eq: r^2 + 1= 0, r = +/- i x(t) = A cos(t) + B sin(t) How do I go about calculating y(t), which th book shows as...
  45. P

    Engineering First order circuits, Inductors

    Homework Statement A security alarm for an office building door is modeled by the circuit [below]. The switch represents the door interlock, and v is the alarm indicator voltage. Find v(t) for t>0 for the circuit [below]. The switch has been closed for a long time at t=0-...
  46. R

    Engineering Solved: RC First Order Circuit Voltage Drop after Switch Opens

    Homework Statement Find the voltage drop across the capacitor just after the switch is opened v(0+) Most variables are in picture attached C = 100mF Homework Equations Vc(t)= Vc(\infty)+[Vc(t+)-Vc(\infty))*e-(t-t1/\tau) The Attempt at a Solution First i assumed that the...
  47. M

    Reducing Second Order ODE system to First Order

    Homework Statement A 3-storey building can be modeled as a system of coupled masses and springs as showen in attached document. Where mi is the mass of each floor, ki is the spring constant, xi is the displacement of each floor, and ci is the damping coeffcient.Homework Equations I understand...
  48. B

    Solution to pde with directional derivative first order

    Homework Statement trying to solve v.\nabla_x u + \sigma(x) u = 0 (x,v) \in \Gamma_- \Gamma_- = \left\{(x,v) \in X x V, st. -v.\nu(x) > 0\right\} \nu(x) = outgoing normal vector to X v = velocity u = density g(x) = Incoming boundary conditions The Attempt at a...
  49. S

    Understanding Separable Differential Equations and Initial Value Problems

    Homework Statement I am stuck on these two questions. The first one I can start off and finish but i cannot do the middle part and in the second question I have no idea how to start it off. Find the general solution of the following separable equations; then use the solution which obeys...
  50. C

    Engineering Help solving First Order RL circuit

    http://img713.imageshack.us/i/39642770.jpg At time t = 0_ The circuit looks like the voltage source in series with R1 and R2 with the inductor acting like a short circuit. iL (0_) = 60V/50Ω = 1.2A At t = 0+ The circuit looks like http://img839.imageshack.us/i/52735488.jpg...
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