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. B

    First Order, Non-Linear DE - Not Seperable

    Hello, I'm studying for a test and this is a question on a practice test... cos(x)+y^2+(2yx-1)y'=0 I can't separate the variables (it's not homogeneous, either), this isn't exact and bernoulli won't work... dy/dx=-cos(x)/(2yx-1)-y^2/(2yx-1) I changed the equation so it would look...
  2. K

    Help Thrid second and first order differential equation

    Help! Thrid second and first order differential equation! I have no idea how to accomplish this problem. If anyone knows help please help me solve this example before I take my test! Solve y''' - y'' - y' + y - x = 0
  3. C

    MHB Integration of a First order for physical application

    Hello everyone. I wish to get the solution to the following: x'(t) = [A*exp(B*t)-C]^(m) I can get the plotted solution by Matlab, but I wish to find the analytic solution by myself. Does anyone has some hints to help me in this? Thanks a lot for your help /Crevoise
  4. T

    Transforming a system of PDEs into a first order system of ODEs

    Homework Statement Say we have a system of N PDEs, each with even order. That is, say the k^{th} equation has order 2 m_k. If m_i = m_j for all i and j, then we can transform the system of PDEs into a first order system of ODEs by introducing new variables. However, if m_i \neq m_j for some...
  5. D

    Interval Restriction on Solutions to First Order Linear Equation

    I took a picture of a simple problem from my Diff Eq book. It is split up into two pictures for better resolution. In summary, ty'+2y=4t^2 (1) Has the solutions, y=t^2+C/t^2 (2) So, equation (1) has infinite solutions of the form of (2). But imposing the initial...
  6. D

    Solving First-Order Logic Problem with Valuation Existence

    I have a problem I can't quite figure out: I have a first order system S, and an interpretation I of S. I have to show that a closed well formed formula B is true in I if and only if there exists a valuation in I which satisfies B. I've done one of the two implications, but I still have...
  7. A

    Re-write as a system of first order ODEs

    hello, I am going through the first chapter (a review chapter) of a second-course book in ODEs, and can't seem to remember how to re-write higher order DEs into a system of first order linear ODEs, and my old textbook only shows this for second order equations... The question is: "Write the...
  8. I

    Can’t get a start on solving a first order differential equation

    Homework Statement Am looking at a first order, non linear differential equation. I want to solve for a general solution and will have to find a constant with given parameters. Equation: 3x2y+8xy2+(x3+8x2y+12y2)dy/dx=0 Parameters: y(2)=1Homework Equations ∂M/∂y=∂N/∂x (Exactness) & (My-Nx)/N...
  9. R

    Solution of two first order differential equation with one algebraic equation.

    Dear Friends i am trying to solve two first order differential eqs. with one algebraic eq. i am able to get solution of problem by simply solving two first order differential eqs. i do not know how to incorporate algebraic eq with my solution. please see attachment thanks in advance Ricky
  10. R

    Understanding First Order Linear Differential Equations: Solving and Simplifying

    Homework Statement The Attempt at a Solution I don't understand in step one why the three in the numerator disappears. I also don't understand why dy/dx becomes d/dx. the book just says left side is d/dx(v*y), a lot of help that is. how do you go to two fractions with x^3 and x^4...
  11. R

    Why Does dy Change in Solving Linear Differential Equations?

    Homework Statement I don't understand why in step 2 dy turns into d and why +P(x) dissappears I also don't see a difference between v(x)y and v(x)*y In step three why does the d disappear. I see that dx is going over to the right side, well, what about the numerator d?
  12. S

    Reduce second order diff equation into series of first order diff equations

    Hi guys I was hoping if someone could help me with this second order differential equation which i have to reduce into a series of first order equations and then solve using a fourth order runge kutta method. The equation is y"-30y'-3y=-2 with the initial conditions y(1)=-12 and...
  13. A

    First order non-linear non-homogeneous DE problem

    Hello. I am trying to solve this problem methodically but my solution does not seem to agree with the given answer. Homework Statement The differential equation is: (sinx)y' - (cosx)y = 1 + C Homework Equations The Attempt at a Solution y' - (cosx/sinx)y = 1/sinx + C/sinx When finding the...
  14. C

    The angle of the first order diffraction

    Homework Statement What is the angle of the first order diffraction, m=1, when X-rays diffract from a crystal in which a spacing between atomic planes is 0,175nm? The 2nd diffraction, m=2, occurs at 45o. Homework Equations Δr=2dcosθm=mλ m+1/m = cos45/cosθm , because when the m...
  15. L

    First order linear ode, initial condition problem

    hey, i'm having trouble with this question, x y' - y = x2cosx the solution is y= xc + xsinx and we are asked to solve the equation in the following two cases, 1, y(0)=0 and 2, y(0) = 1 but applying these conditions to the general solution gives no information, in...
  16. B

    Categorize first order differential equation

    Homework Statement I'm trying to determine which categories various first order differential equations fall into (and once they're categorized they're nice and easy to solve). My list of categories is the following; linear equations, homogenous equations, bernoulli equations, exact equations...
  17. T

    Solving First Order Linear Differential Equation

    Homework Statement Given (E): (x+1)^{2}(xy'-y) = -(2x+1) Determine the set of applications from the interval I to ℝ which are solutions of (E) for: a) I = (0,+∞) b) I = (-1,0) c) I = (-∞,-1) d) I = (-1,+∞) e) I = ℝ The attempt at a solution I have...
  18. E

    Integral of spherical bessel function (first kind), first order

    Hello, I am trying to solve the following integral (limits from 0 to inf). ∫j_1(kr) dr where j_1 is the first order SPHERICAL Bessel function of the first kind, of argument (k*r). Unfortunately, I cannot find it in the tables, nor manage to solve it... Can anybody help? Thanks a lot! Any...
  19. B

    First order differential equations.

    Hi, I have problems rewriting equations with the term y'' as a system of first order differential equations. I've been given several equations and was told to write them as 1st order DEs, then calculate the numerical solution using the Euler's modified method. I know that y'=f(x,y), so if...
  20. H

    Coupled first order differential equation.

    Homework Statement \frac{dx}{dt}=\gamma y \frac{dy}{dt}=-\gamma x solve for x and y Homework Equations The Attempt at a Solution I know how to solve it by substitution(without using matrix) I know how to solve a coupled second order differential equations in matrix form, but not...
  21. Telemachus

    Covariant Tensor first order, and antisymmetric second order

    Hi there. This is my first time working with tensors, so I have to break the ice I think. I have this exercise, which I don't know how to solve, which says: If V=V_1...V_n is a first order covariant tensor, prove that: T_{ik}=\frac{\partial V_i}{\partial x^k}-\frac{\partial V_k}{\partial x^i}...
  22. O

    First Order, Second Degree ODE

    Homework Statement Solve y^2*(1-(dy/dx)^2)=1 Homework Equations The Attempt at a Solution I expressed the ODE in terms of dy/dx and considered two cases. I got (a) y^2 = 1 + (x+C)^2 (b) y^2 = 1 + (-x+C)^2 where C is a constant However, my professor told me that there is...
  23. J

    Initial value problem, first order linear ode

    Hey, We haven't properly covered this in class yet, but I am trying to study ahead using online course notes, I manage to finish a few questions but I have gotten stuck here, The question starts by asking for the solution to the ODE: y' = 1 - 2xy, When I solve this using the...
  24. H

    Solving nonlinear first order DE w/ fractional exponents

    Hello. I have simple DE y' + p y^(1/2) = q --------------- y'=dy/dt p,q=constant I am confused because I tried bernoulli's method to solve and I think I exploded the universe. Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there...
  25. S

    First order non linear boundary value pb

    Hi there: I am trying to solve a two points boundary value problem. Consider a function f:[x1,x2]->[x2,x3] x1 and x3 are knowns x2 is an unknown parameter f'(x) = exp( -a*x + b*f(x) ) where b>a>0 Two boundaries conditions: f(x1) = x2 f(x2) = x3 Does anyone know how to...
  26. M

    Confusing question in Differential first order

    Q) I have a first order ODE of the form dy/dx = F(ax+by+c)/(Ax+By+C) ---> (a,b,c,A,B,C all non zero constants) Under what condition, does there exist a linear substitution that reduces the equation to one in which the variables are separable? (A) Never (B) if aB = bA (C) if bC = cB...
  27. J

    About simple first order differential equation

    Homework Statement dy/dx = (3x^2+4x+2)/2(y-1) , y(0)=1 Homework Equations The Attempt at a Solution I get the answer and the steps are shown: 2(y-1)dy=(3x^2+4x+2)dx and integrate both sides y^2-2y=x^3+2x^2+2x+c By initial condition, c=-1 and by solving for y, y =...
  28. M

    MHB Solving First-Order PDE: $u_x+2u_y+2u=0$

    Solve $u_x+2u_y+2u=0,$ $x,y\in\mathbb R$ where $u(x,y)=F(x,y)$ in the curve $y=x.$ I don't know what does mean with the $y=x.$ Well I set up the following $\dfrac{dx}{1}=\dfrac{dy}{2}=\dfrac{du}{-2} ,$ is that correct? but I don't know what's next. Thanks for the help!
  29. F

    Quotient of First Order Ordinary Derivatives

    How do you solve (analytically or numerically) a differential equation of this form, $$\frac{\mathrm{d}y(x)/\mathrm{d}x}{\mathrm{d}z(x)/\mathrm{d}x} = a[1-y(x)-z(x)] + b$$ where a, b are constants. Also, $$y(0) = z(0) = 0$$
  30. D

    Exact equations. first order DE. finding f (x,y)

    I go to a community college. So my professor taught us exact equations: how to test it and how to solve them. I want the forum to give me examples of a exact DE that my professor is talking about, reinforce her or my idea or method, or explain to me if I truly am wrong. We used M and N for...
  31. W

    First order seperable ode with IC's

    Homework Statement Question According to Newton’s Law of Cooling, the rate at which a substance cools in air is proportional to the difference between the temperature of the substance and that of air. The differential equation is given byAccording to Newton’s Law of Cooling, the rate at which...
  32. T

    Separable First Order Differential Equation

    Homework Statement \frac{dy}{dx} = y \sqrt{x} , f(9) = 5 The Attempt at a Solution \int dy/y = \int \sqrt{x} dx ln |y| = \frac{2}{3} x^\frac{3}{2} + c y = e^{\frac{2}{3}x^\frac{3}{2}} + C y = Ce^{\frac{2}{3}x^\frac{3}{2}} 5 = Ce^{\frac{2}{3}9^\frac{3}{2}} 5 =...
  33. W

    Solving a first order DE using integrating factor method

    Homework Statement (3(x^2)y + 2xy + y^3)dx + (x^2 + y^2)dy = 0 The Attempt at a Solution This is from my notes, so I already have the answer. I just don't understand the very last step with the integrations. (3(x^2)y + 2xy + y^3)dx + (x^2 + y^2)dy = 0 My = 3x^2 + 2x + 3y^2 Nx = 2x...
  34. P

    How Does Opening a Switch Affect a Circuit with a Capacitor and Resistors?

    Homework Statement http://imgur.com/VsDrQ,dJ2iv Homework Equations Current in loop 1: i_1 going counter-clockwise Current in loop 2: i(t) going counter-clockwise Before opening switch: we know that 2 loops exist, left and right. also the current is constant because it says the...
  35. J

    Eigenvalues for Equilibrium Points of First Order Nonlinear DE

    Homework Statement dy/dx = y^3-3y^2+2y it's asking for equilibrium points and for the eigenvalues and stability at each point. Homework Equations The Attempt at a Solution I found the equilibrium points by setting dy/dx = 0 as we were taught to do in class and got y = 0, 1, 2...
  36. D

    HELP First Order DE using Substitution Method

    I feel as if I have made the correct substitution, what am I missing? See Attachment. Thanks, Dane
  37. C

    Ugly first order differential equation

    Homework Statement solve the differential equation: (1+t^2)y'+4ty=(1+t^2)^-2Homework Equations μ=exp∫adt The Attempt at a Solution this problem gets quite ugly, so here goes. first question does μ=e^(1+t^2)^2
  38. A

    Is there a better way of solving this first order linear differential equation?

    3y'+2y-2sin(3x)+2e(-3x)+x3+4=0 Variables x - independent y - dependent Attempt at a solution I rewrote the equation in form dy/dx+P(x)y=Q(x) and used an integrating factor of \mu(x)=ke(2/3)x with P(x) = 2/3 and Q(x) = 2sin(3x)-2e(-3x)-x3-4 Since y(x) =...
  39. M

    MHB Solving First Order PDEs: Laplace, Fourier & Separation of Variables

    1) $u_x+u_y=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=\cos x,\,x\in\mathbb R.$ 2) $xu_x+u_y+uy=0,\,x\in\mathbb R,\,y>0$ and $u(x,0)=F(x),\,x\in\mathbb R.$ 3) Solve the following equation $2xu_y-u_x=4xy,$ where the initial curve is given by $x=0,\,y=s,\,z=s.$ ------------------------- 1) Laplace...
  40. M

    MHB Solve 1st Order PDE: $u_y+f(u)u_x=0$

    Solve $u_y+f(u)u_x=0,$ $x\in\mathbb R,$ $y>0,$ $u(x,0)=\phi(x).$ What's the easy way to solve this? Fourier Transform? Laplace Transform?
  41. J

    Linear First Order Differential Equation - Mixture Problem

    The problem and attempt at solution are typed below
  42. QuarkCharmer

    First order non-separable linear deq's using an integration factor?

    For example: \frac{dy}{dx} + y = e^{3x} I understand that these differential equations are most easily solved by multiplying in a factor of integration, and then comparing the equation to the product rule to solve et al.. For example: t\frac{dy}{dx} + 2t^{2}y = t^{2} \frac{dy}{dx} + 2ty = t...
  43. M

    First order linear differential equations

    Homework Statement dy/dt=y((3t^2)-1), y(1)=-2 Homework Equations Basic integrals The Attempt at a Solution integrate on both sides: dy/y=dt((3t^2)-1) ========>ln(y)=(t^3)-t+c ========>y=e^((t^3)-t+c) ========>y=e^((t^3)-t)e^(c) I am not sure if its some e rule that I forgot...
  44. S

    Engineering First order responce; RC circuit

    Homework Statement Assume there is a voltage source in series with a resistor and a capacitor. Thus, V_S=i(t)R+v_C(t)=CR\frac{dv_C}{dt}+v_C\rightarrow{}dt/(RC)=dv_C/(V_S-v_C) From this point I understand that one has to apply a negative sign to both sides before integrating, but why is it...
  45. T

    Is this a legitimate method for solving first order ODEs in fractional form?

    Suppose we have some ODE given by y' = G(x,y)/H(x,y). Let x and y depend on a third variable, t, so that x and y are parametrized in a way. Then applying the chain rule to y' gives \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{G(x,y)}{H(x,y)} Then comparing the numerators and...
  46. E

    How to Differentiate Between First Order and Second Order Processes?

    How can i differentiate between first order & second order ??!
  47. T

    Solving a Non-Homogeneous First Order Linear DE System

    Homework Statement I need to solve this DE system for a lab: q_1'=2-\frac{6}{5}q_1+q_2 q_2'=3+\frac{3}{5}q_1-\frac{3}{2}q_2Homework Equations The Attempt at a Solution I know how to use the method of elimination to solve such systems, but this is non homogeneous because of the added constant...
  48. I

    Landau theory: why does a m^3 term implies first order transition phase

    Hi, I am not sure it is the right subcategory to post a question on statistical physics. But anyway, I read a couple of times that adding a m^3 to the Landau free energy implies that we may observe a first order transition phase, but I don't see why. Maybe it does imply some discontinuity in...
  49. S

    First order PDE with two conditions?

    Hello, I have a problem in the form \frac{\partial u}{\partial t}+\frac{\partial u}{\partial x}+e^{x}u=0 with conditions u(x,0)=u_0(x) u(0,t)=\int_{0}^{\infty}f(x)u(x,t)dx Im confused, because in first order PDE i require only 1 condition. How to solve this for two conditions?
  50. C

    First Order Nonlinear Partial Differential Equation

    I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by: dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant) v(t = 0) = C (constant value) v(x = 0) = 0 I'm not quite sure how to solve this. I was thinking about using the method of...
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