Graph and manipulate DSolve result

Question

Given a DSolve example:

sol = Flatten[
DSolve[{D[x[t, th], {t, 2}] == -0.2*D[x[t, th], t]/2.30, 
 Derivative[1, 0][x][0, th] == 10.8*Cos[th], x[0, th] == 0}, 
x[t, th], t]]

Then assigning sol to a function:

 x[t,th]/.sol[[1]]

I'm having trouble plotting a 2D portion of it:

Plot[x[t,1],{t,0,20}]

And also trouble Manipulating it:

Manipulate[x[t,th], {th, 0, Pi/2}]

What mistakes am I making?

Answer 1

I'm not sure what you think x[t,th]/.sol[[1]] does. From your question, Here is what I think you're trying to accomplish.

sol = Flatten[  DSolve[{D[x[t, th], {t, 2}] == -0.2*D[x[t, th], t]/2.30, 
    Derivative[1, 0][x][0, th] == 10.8*Cos[th], x[0, th] == 0}, 
   x[t, th], t]];

x[t_, th_] = sol[[1, 2]]; (* This defines the function using the solution from DSolve *)

To get the Plot do the following:

Plot[x[t, 1], {t, 0, 20}] 

To Manipulate, do the following:

Manipulate[Plot[x[t, th], {t, 0, 100}, PlotRange -> {{0, 100}, {0, 130}}], {th, 0, Pi/2}]

Hope this helps.