How do I plot the solution of a differential equation?

Question

I am unable to plot the solution to this differential equation in Mathematica representing the current in a RLC circuit with a sinusoidal input.

L*y''[t] == -R*y'[t] - C*y[t];
(*V\[Equal]Sin[t];*)
soln = DSolve[{L*y''[t] == -R*y'[t] - C*y[t], y[0] == 0, y'[0] == V}, 
     y[t], t][[1]] // Simplify;

With[{expr = y[t] /. soln}, 
 Manipulate[
  Plot[expr, {t, 0, 2*Pi}, 
   PlotRange -> {{0, 10}, {-5, 5}}], {{L, 1*^-3}, 0, 
   10*^-3}, {{R, 3*^3}, 1*^3, 10*^3}, {{C, 3*^5}, 0, 10*^5}, {{V, 5}, 
   0, 10}]]

I think my problem is either in defining my Differential equation or plotting. Any ideas?

Answer 1

Here is just the case when the exact solution is worse than numerical. Therefore, we solve numerically

 Manipulate[
 Plot[Evaluate[
   y[t] /. First[
     NDSolve[{L*y''[t] == -R*y'[t] - C0*y[t] + V*Sin[t], y[0] == 0, 
       y'[0] == V}, y, {t, 0, 2*Pi}]]], {t, 0, 2*Pi}], {{L, 1*^-3}, 
  10^-6, 10*^-3, Appearance -> "Labeled"}, {{R, 3*^3}, 1*^3, 10*^3, 
  Appearance -> "Labeled"}, {{C0, 3*^5}, 0, 10*^5, 
  Appearance -> "Labeled"}, {{V, 5}, 0, 10, Appearance -> "Labeled"}]