Hi Mattias,

there are several problems with your input:

1. The Function DSolve is written with a capital S.
2. The function you want to use here is NDSolve.
3. You use e^ which is not correct. e is either Exp[1] or you wrap Exp around the exponent or you use the special symbol or use E, but not simply e.

This piece of code should work:

Equation1 = 
 NDSolve[{L''[t] == (((0.01*4 ?*10^-7*L[t]*(440*Exp[1]^(-t/(0.5*0.0025)))^2/?)*(0.01^2 + (L[t]^2 - L[t]*Sqrt[0.01^2 + L[t]^2]))/
         Sqrt[0.01^2 + L[t]^2])/0.01), L[0] == 0.001, L'[0] == 0.01}, L, {t, 0, 0.1}]

You can plot it like so:

Plot[L[t] /. Equation1, {t, 0, 0.1}]

which gives

Cheers, Marco

Dear Mattias,

no that is not the problem, I believe. I think that Mathematica treats your equation quite correctly. The solution looks rather straight because of your parameters. If you use different parameters:

Equation1 = 
 NDSolve[{L''[
     t] == (((0.1*4 ?*10^-1*
          L[t]*(440*Exp[1]^(-0.001 t/(0.5*0.0025)))^2/
           ?)*(0.01^2 + (L[t]^2 - L[t]*Sqrt[0.01^2 + L[t]^2]))/
         Sqrt[0.01^2 + L[t]^2])/0.01), L[0] == 0.1, L'[0] == 0.01}, 
  L, {t, 0, 0.1}]

looks not that linear anymore:

I think that for your parameters the straight line is a good approximation in your domain, but the result is strictly speaking not a straight line.

Cheers, Marco