Plotting the solution of an ODE

[Robin04]

I'm trying to plot the solution to an ODE (with given initial values) but there are some constants in it that I want to evaluate with sliders and I'm not sure what is the right syntax for this.

Manipulate[Plot[solution1[t], {t, 0, 10}, PlotRange -> {-Pi, Pi}],
{{a, 1, "Driving amplitude"}, 0, 10, Appearance -> "Labeled"},
{{g, 9.81, "Gravitational acceleration"}, 0, 10,
  Appearance -> "Labeled"},
{{l, 1, "Length"}, 0, 10, Appearance -> "Labeled"},
{{\[Gamma], 1, "Driving frequency"}, 0, 10, Appearance -> "Labeled"}]

If I copy solution1 explicitly into plot it works, but if I refer to it by the variable name it doesn't. What's the correct syntax for this?

 

[jedishrfu]

This post mentions using NDsolve for these kinds of problems with sliders:

https://mathematica.stackexchange.com/questions/84192/using-ndsolve-within-manipulate

and I found this neat looking reference:

https://coen.boisestate.edu/bknowlton/files/2011/12/Mathematica-Tutorial-Megan-Frary.pdf

 

[Dale]

I have found the same problem with Manipulate. I have not found a way around it.

 

[Bill Simpson]

I have had consistent success with putting all the needed definitions and functions inside the Manipulate

Manipulate[
sol=p[t]/.DSolve[{a p''[t]==p[t],p[0]==0,p'[0]==a},p[t],t][[1]];
Plot[sol,{t,0,4}],
{{a,1},0,4}
]