What is Ordinary differential equation: Definition and 96 Discussions

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

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  1. khurram usman

    A discussion about Fourier and Laplace transforms and calculus

    i have read many of the answers and explanations about the similarities and differences between laplace and Fourier transform. Laplace can be used to analyze unstable systems. Fourier is a subset of laplace. Some signals have Fourier but laplace is not defined , for instance cosine or sine...
  2. Remixex

    Who Wins the Drag Race Based on Constant Acceleration?

    Homework Statement I stumbled upon a problem and i can't establish the ODE to solve it, from there on i believe i can solve the ODEs if they have regular analytical solving methods (translated from Spanish, will sound a bit weird) Car race, 2 pilots (a and b) participate in a drag race. They...
  3. Prof. 27

    Linear Ordinary Differential Equation: Definition

    Homework Statement The website says this: "It is Linear when the variable (and its derivatives) has no exponent or other function put on it. So no y2, y3, √y, sin(y), ln(y) etc, just plain y (or whatever the variable is). More formally a Linear Differential Equation is in the form: dy/dx +...
  4. L

    Nonlinear Ordinary Differential Equation Help

    Homework Statement y'=(x^2 +xy-y)/((x^2(y)) -2x^2)[/B]Homework EquationsThe Attempt at a Solution I know that really the only way to solve this one is to use an integrating factor, and make it into an exact equation. My DE teacher said that to make it into a exact equation you need to take...
  5. Greg Bernhardt

    What is a linear ordinary differential equation

    Definition/Summary An nth-order linear ordinary differential equation (ODE) is a differential equation of the form \sum_{i=0}^n a_i(x)y^{(i)}(x)\ =\ b(x) where y^{(i)}(x) denotes the ith derivative of y with respect to x. The difference between any two solutions is a solution of the...
  6. AntSC

    Ordinary Differential Equation - Comparing 2 Solutions

    Homework Statement {g}'\left ( s \right )+\mu g\left ( s \right )={f}'\left ( -s \right )+\mu f\left ( -s \right ) Integrate up to get g\left ( s \right )=-f\left ( -s \right )+2\mu e^{-\mu s}\int_{-s}^{\infty }e^{-\mu {s}'}f\left ( {s}' \right )d{s}' Homework Equations As above...
  7. K

    MHB Homogeneous, linear, first-order, ordinary differential equation mistake

    I am trying to solve a homogeneous, first-order, linear, ordinary differential equation but am running into what I am sure is the wrong answer. However I can't identify what is wrong with my working?! $$\frac{dy}{dx}=\frac{-x+y}{x+y}=\frac{1-\frac{x}{y}}{1+\frac{x}{y}}.$$ Let $z=x/y$, so that...
  8. N

    Analytical solution of nonlinear ordinary differential equation

    Dear All, I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution. \frac{dx}{dt} = 2Wx + 2xy - 4x^{3}\frac{dy}{dt} = \gamma \, (x^{2} -...
  9. C

    Solution of an Ordinary Differential Equation

    Hi, The definition (see attachment) says that f(x) is a solution to the differential equation if it satisfies the equation for every x in the interval. Assuming that I have a differential equation that I want to solve and the D.E. has an interval I_1, and I've come up a solution with...
  10. C

    MHB First Order Nonlinear Ordinary Differential Equation

    Hello, can you guys help me please with this differential equation from Demidovitch book, is to find the solution transforming to polar coordinates :
  11. A

    Question on Ordinary Differential Equation (ODE)

    Homework Statement Find the ODE of the following (1) du/dy = -u (2) d^2u/dxdy = -du/dx Homework Equations For question 1, the answer is u= A(x)e^(-y) while for question 2, the answer is u= e^(-y)(B(X) + c(Y)) The Attempt at a Solution I've already solved the question, but...
  12. S

    First-order nonlinear ordinary differential equation

    hii, how to solve this differential equation: A*(dT(x)/dx)(1873.382+2.2111T(x))=90457.5-2.149*10^-10* (T(x))^4 where A is a constant Thank you
  13. S

    Ordinary Differential Equation

    Homework Statement Homework Statement Solve \frac{dz}{dt} + 3 t e^{t+z} = 0 Homework Equations None that I can think of... The Attempt at a Solution "Rearranging" the given question, we get: \int \frac{dz}{e^z} = -3\int t e^t dt -e^{-z} = -3 \left( t e^t - e^t \right)...
  14. S

    Homogenous Ordinary Differential Equation

    Homework Statement x2y"-(x2+2x)y'+(x+2)y=0 known solutions: y1(2)=2 y1'(2)=1 y2(2)=2e2 y2'(2)=3e2 Determine the wronskian Homework Equations yc=C1er1x+C2er2x I also know how to find the wronskian via a determinant The Attempt at a Solution I have tried to divide out...
  15. T

    Solving an ordinary differential equation.

    Homework Statement Here is an example from the book: https://dl.dropbox.com/u/64325990/MATH%20255/EX%204.PNG Does anyone know why they chose t to be equal to 0? Thanks!
  16. H

    Trouble solving an ordinary differential equation

    Homework Statement Find the appropriate equation. Homework Equations So there we have the ordrinary differential equation \frac{d M}{dt}=k_1M-k_2(1-M)=A\exp \left (-\frac{E}{T} \right )M-B\exp \left ( -\frac{F}{T} \right )(1-M) The goal is to solve the differential equation. It...
  17. D

    How to solve this second-order nonlinear ordinary differential equation?

    I was trying to solve a calculus problem (about the equation of the curve traced by a dog chasing a postman) and I came across the following equation. I would like to know how to solve it. \frac{w}{v}(1-\frac{y(x)y''(x)}{{y'(x)}^{2}})=\sqrt{1+{y(x)}^{2}}-\sqrt{1+{C}^{2}} Thanks.
  18. 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.
  19. 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}...
  20. D

    Asymptotes for numerical solution of ordinary differential equation

    Hi! I have a differential equation coming from Boltzmann transport equation which is a bit complicated and should be solved numerically instead of analytically. I managed to get a plot using Runge-Kutta with software Derive. The equation is in the second attachment. In the papers of my...
  21. T

    Solving ordinary differential equation

    Hi guys! Attached is the differential equation that I want to solve both numerically and analytically, numerically done. But analytically what method could I use? There is so many methods in differential equations. Please advice on this. Thank you very much
  22. C

    Ordinary Differential Equation System with Variable Coefficients

    Homework Statement For t\in\mathbb{R}, let: A=\left[\begin{array}{ccc} -1 & 0 & 0\\ 0 & 2 & 2t\\ 0 & 0 & 2\end{array}\right] Get the solution for the general equation: X'=A(t)X Homework Equations The Attempt at a Solution I done many of these problems, all with constant...
  23. E

    Simple Differential Equation (Ordinary Differential Equation)

    Problem: y'+2y=4(x+1)2 ----> y=5e-2x+2x2+2x+1 1. What the Order of the ODE? It's 1st order 2 How do you check whether a particular function solves an equation? If you solve y'+2y=4(x+1)2 and make it y=5e-2x+2x2+2x+1. I want the whole solution... thanks...
  24. A

    Particular Solution to a Second Order Ordinary Differential Equation

    Homework Statement Find the Particular Solution to the differential Equation satisfying the initial conditions. y''+7y'+10y= -30 y(0)= 3 y'(0) = -27Homework Equations Characteristic Equation for Homogenous Solution y''+7y'+10y=0 roots are -2 and -5 General Solution is C1e^-2t + C2e^-5t...
  25. M

    First order nonlinear ordinary differential equation

    Homework Statement y' + Ay2 = B A & B are constants and y is a function of x Find the general solution to the differential equation. (Find y(x)). Homework Equations The Attempt at a Solution This differential equation came up when I was trying to solve a problem in...
  26. E

    How Do You Solve \(\dot y(x) - 2y(x) = y^2(x)-3\) in Differential Equations?

    Homework Statement I need to find a general function y(x) such that: \dot y(x) - 2y(x) = y^2(x)-3 Homework Equations The Attempt at a Solution I tried dividing the equation by y^2-3 and turn it into a Bernoulli differential equation, but that didn't work. The equation seems...
  27. C

    Ordinary Differential equation

    Homework Statement Note: Here your solution is implicitly defined, i.e. you can not rearrange the solution to get an explicit expression for y. Therefore you need to enter your solution as an equation. You should enter your solution in the form f(x,y) = constant where you have determined both...
  28. L

    A second order nonlinear ordinary differential equation

    How, if possible, could I solve the equation: x''x=((x')^2)/2? Thanks.
  29. W

    How to integrate an ordinary differential equation around a singular point?

    i have a second order ordinary differential equation of f(x): f''+(E-A(A+1)/x^2)f=0, where A is a positive integer, E is a real constant the domain is [0, \infty). the boundary condition is f(x=0)=0 since this is a linear equation, i only need to determine f up to a overall constant...
  30. M

    Solution to ordinary differential equation

    why is the 4th order Runge -Kutta method widely used than the 2nd or 3rd,for solving ordinary differential equations?
  31. B

    Problem with first-order nonlinear ordinary differential equation

    i have problem to find the solution for : (3x3y+2xy+y3)+(x2+y2)dy/dx=0 i have tried the exact equation method : (3x3y+2xy+y3)dx+(x2+y2)dy=0 thus M(x,y)=(3x3y+2xy+y3) and N(x,y)= (x2+y2) then deltaM/deltay=3x3+2x+3y2 and deltaN/deltax=2x Since deltaM/deltay does not equal to...
  32. N

    Verify that this is the solution to an ordinary differential equation

    Homework Statement I am given dy/dt -2yt = 1 and y(t) = (e^(t^2))[e^(-s^2)ds] + e^(t^2) integrate from t to 0 within the brackets. Homework Equations The Attempt at a Solution I know that the derivative of y(t) would equal e^(t^2) However I do not know how I am supposed to solve...
  33. N

    What ordinary differential equation? Simple answer is needed

    What ordinary differential equation? Simple answer is needed! Homework Statement instead [delta] i will use 'd'. in these two example, what kind of ordinary dif. eq. are implied by the methodd of separation of variables. first one is; du/dt=(d^2u)/(dx^2) - 5 du/dt and other one is...
  34. L

    Second-order nonlinear ordinary differential equation

    Homework Statement Given the Second-order nonlinear ordinary differential equation x''(t)=1/(x(t)^2) Find x(t).Homework Equations I tried use Laplace transforms, and solving it using linear methods but that is not useful.The Attempt at a Solution I tried to find t(x) and got to...
  35. E

    Ordinary Differential Equation Series Solution

    Homework Statement y' = \sqrt{(1-y^2) } Initial condition y(0) = 0 a) Show y = sinx is a solution of the initial value problem. b) Look for a solution of the initial value problem in the form of a power series about x = 0. Find coefficients up to the term in x^3 in this series. Homework...
  36. P

    First order Ordinary Differential Equation

    Homework Statement Solve the differential equation: y' = 8sin(4yt) ; y(1) = 4 Homework Equations The Attempt at a Solution The integrating doesn't apply because I can't get the equation into: y' + p*y = f(x) form Also, I have tried separating variables, but I can't get the y inside of the...
  37. W

    Ordinary Differential Equation by substitution.

    Homework Statement dy/dx = (x+3y)/(3x+y) I have to solve the given differential equation by using an appropriate substitution... The Attempt at a Solution I used algebra to make the equation (3x+y)dy - (x+3y)dx = 0 then made x = vy and dx = vdy + ydv. then plugged into get...
  38. T

    General solution of ordinary differential equation

    Homework Statement Find the general solution of the differential equation, y' + y = be^(-λx) where b is a real number and λ is a positive constant. Homework Equations y' + P(x)y = Q(x) Integrating factor: e^(∫P(x) dx) The Attempt at a Solution Let P(x) = 1, Q(x) =...
  39. H

    General solution of a linear ordinary differential equation

    Hi all. Can the general solution of a linear ordinary differential equation be expressed in terms of its initial conditions? It seems that I have seem this kind of representation. It makes "some sense" to me but I hope to know if there is some "proof" or explanation of why it can be? To be...
  40. L

    Solving an Ordinary Differential Equation Problem: x*x''-y*y''=0

    I have been looking though Ince (Ordinary Differential Equations), nice book. I enjoyed solving this problem: 6) pp. 157 Integrate the system x*x''-y*y''=0 x''+y''+x+y=0 [Edinburgh, 1909.] we may assume x and y are twice differentiable functions defined everywhere from reals to reals...
  41. T

    Help with nonlinear ordinary differential equation

    Any help with solving this first-order nonlinear ODE would be greatly appreciated! I do believe that an explicit solution exists. Homework Statement dy/dt = 1/(4t^2) + 1/2 + 1/2*y/t - 1/(2t)*((1+4ty)^(1/2)) I was led to believe that it could be solved by turning it into a linear...
  42. R

    Ordinary differential equation question

    Homework Statement What is the general solution to the following ODE F=X''m where F and m are both constants Homework Equations The Attempt at a Solution I got X=(k/2)t^2 + C I got this from F/M being just another constant K, and X'' being (d^2 X)/(dt^2) so you just...
  43. E

    Ordinary differential equation:

    Homework Statement Obtain the general solution: (1 - x)y' = y^2 Homework Equations The Attempt at a Solution (1 - x)\frac{dy}{dx} = y^2 (1 - x)dy = y^2dx \frac{dy}{y^2} = \frac{dx}{(1-x)} integrating both sides: i used ln on the constant at the right side -\frac{1}{y}...
  44. A

    Arndol's ordinary differential equation

    how different are the spring versions and the mit press version? also, what is the difference between https://www.amazon.com/gp/product/0387548130/?tag=pfamazon01-20 and https://www.amazon.com/dp/3540345639/?tag=pfamazon01-20 thanks
  45. H

    2nd order ordinary differential equation for damped harmonic motion

    Homework Statement the equation of motion for a damped harmonic oscillator is d^2x/dt^2 + 2(gamma)dx/dt +[(omega0)^2]x =0 ... show that x(t) = Ae^(mt) + Be^(pt) where m= -(gamma) + [(gamma)^2 - (omega0)^2 ]^1/2 p =-(gamma) - [(gamma)^2 - (omega0)^2 ]^1/2 If x=x0 and...
  46. C

    Ordinary differential equation

    what is the word ordinary mean? Why is it called so. Am i correct to say that the solution of a differential equation is got by integrating that equation.
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