# Differential Equation and Mathematica

1. Apr 26, 2007

### b2386

Hi all,

Does anyone know if Mathematica can numerically solve a second order differential equation?

2. Apr 26, 2007

### Dick

Sure can. Look up NDSolve.

3. Apr 26, 2007

### b2386

Well, I have been trying to solve this equation with mathematica for the past two hours with no luck.

The general differential equation I am trying to solve is $$u''_i(T) = .65\frac{u'_{i-1}(T)-u'_{i}(T)}{u_{i-1}(T)-u_{i}(T)}+750(u_{i-1}(T)-u_{i}(T)-1)^3$$ where i= 1,2,3 and $$u'_0(T)=2\pi*Sin(2*\pi*T)$$

The initial conditions are $$u_i(0)=-i$$ and $$u'_i(0)=0$$. I tried using NDSolve but it kept saying that the input was not a differential equation. Does anyone know what should be the syntax of the NDSolve function I need?

Last edited: Apr 26, 2007
4. Apr 26, 2007

### b2386

Well, I finally was able to get the NDSolve to work for this differential equation for T values from 0 to 24 and I set the NDSolve function to the variable "soln". So what function should I use to graph the numerical solutions?

5. Apr 27, 2007

### sigmund

Look into the help browser of Mathematica (press F1) under NDSolve. There should be a list of examples (see 'Further examples'). From this you will also see how to plot the solution provided by NDSolve. See also http://documents.wolfram.com/mathematica/Built-inFunctions/NumericalComputation/EquationSolving/FurtherExamples/NDSolve.html [Broken].

Finally, I should point out, that this question really belongs in the Mathematica newsgroup, found through Google Groups.

Last edited by a moderator: May 2, 2017