Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

I want to plot x[t], when i manipulate w from 0.1 to 1.5. Here is what I've attempted, which does not work as expected.

c = 0.05; f = 0.7;
diffeq = {x''[t] + c x'[t] + Sin[x[t]] + F Cos[w t] == 0};
inicond = {x'[0] == 0, x[0] == 1};
eqnlist = Join[diffeq, inicond];
soln := NDSolve[eqnlist, x, {t, 0, 10}]
            Plot[Evaluate[{x[t] /.soln}, {t, 0, 10}], PlotRange ->All, AxesLabel-> {t, x}], 
          {w, 0.1, 1.5, 0.1}]

What is the appropriate way to plot the numerical solution of a differential equation while varying a parameter?

share|improve this question
And what exactly is your code supposed to do? –  rm -rf Mar 4 at 2:21
@ rm -rf♦ I want to Plot x[t],versus t, when varying w from 0.1 to 1.5. –  Lawerance Mar 4 at 2:22
Can anyone tell me why this post get negative vote? I'm confused and i think everything is clear here. –  Lawerance Mar 4 at 2:30
Welcome to M.SE. I edited your question (heavily) to demonstrate how a question can be formatted. In general, using the formatting guidelines suggested in the help section will generate more favorable responses to your questions. –  bobthechemist Mar 4 at 2:41
@Lawerance It's always a good idea to explain what you're trying to do (i.e., what is this equation) rather than just say you want to plot something from a to b. Your question only had code, no context. As it turned out in this case, the problem had nothing to do with the plotting... Imagine yourself in this position — would you like it or be willing to help if someone just said "Here's a bunch of code. It should do what I want, but it doesn't" without telling you what they want it to do? We can't read minds. Hope you try to take these suggestions constructively for your next question :) –  rm -rf Mar 4 at 2:50

2 Answers 2

This is a good case for ParametricNDSolve:

c = 0.05; f = 0.7;
diffeq = x''[t] + c x'[t] + Sin[x[t]] + f Cos[w t] == 0;
inicond = {x'[0] == 0, x[0] == 1};
sol = ParametricNDSolve[{ 
   x''[t] + c x'[t] + Sin[x[t]] + f Cos[w t] == 0, x'[0] == 0, 
   x[0] == 1}, x, {t, 0, 10}, {w}]
 With[{x1 = x[w] /. sol}, Plot[x1[t], {t, 0, 10}]], {w, 0.1, 1.5}]

Mathematica graphics

share|improve this answer
Next time, how do I tell if it I need Parametric NDSolve or not? –  Lawerance Mar 4 at 2:39
@Lawerance , the documentation will help you out tremendously here. You must provide numerical values for all parameters if using NDSolve, but have the flexibility of varying the parameters with ParametricNDSolve. –  bobthechemist Mar 4 at 2:43

bob's answer is the right one, but I thought I would explain a bit about why your code isn't working. The essential problem is that your expression soln won't work with NDSolve since it has a non-numeric parameter, omega. Setting the value of omega in the Manipulate isn't sufficient to avoid this error. If you just evaluate soln you get this:

NDSolve::nlnum: The function value {-0.00014456,-0.841464-0.7 Cos[0.0000937804 omega]} is not a list of numbers with dimensions {2} at {t,x[t],(x^[Prime])[t]} = {0.0000937804,1.,-0.00014456}. >>

(* {{x->InterpolatingFunction[{{0.,0.}},<>]}} *)

This works:

NDSolve[eqnlist /. omega -> 0.1, x, {t, 0, 10}]
(*  {{x->InterpolatingFunction[{{0.,10.}},<>]}} *)

As an alternative to bob's answer, what I'd suggest is that you change your Manipulate to something like this:

Manipulate[ Plot[Evaluate[
   x[t] /. NDSolve[eqnlist /. omega -> oo, x, {t, 0, 10}], {t, 0, 10}], 
   PlotRange -> All, AxesLabel -> {t, x}], {oo, 0.1, 1.5, 0.1}]

It might be slower for more complex differential equations, but it certainly works in your case.

share|improve this answer
Thanks a lot! Regarding the problem both you and Bob mentioned that NDSolve need the numerical values of all the variables, my question is that when i define "soln", I used ":=", instead of "=". I thought ":=" can hold the function to "Manipualte". –  Lawerance Mar 4 at 2:59

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.