# Mathematica NDSolve different solutions same eq's

1. Jul 23, 2015

### Vrbic

Hello, I have peculiar trouble with mathematica. I'm playing with lagrangians of some systems and I hit on "central problem". If I use my procedure in mathematica it solve 2 eq. of second order. But if you solve it by hand, you know, $\phi$ coord is "cyclic". And second eq. is reduced to $\delta_t (mr^2 \phi)=0$ and we introduce constant of angular momentum $L$.
And the problem: If I let solve mathematica general equation without introduction $L$ I get another solution than if I transform second equation by introduction $L$
(different eq.'s: $2mr\phi'+mr^2\phi''=0$ and $mr^2\phi'=L$)
I used same initial condition.
Could you somebody advise where is the problem or how to resolve it?

2. Jul 23, 2015

### Vrbic

My bad, I found out that, the initial conditions aren't same. But it is for me still mystery. Why for this two same eq.'s in different forms, the initial conditions setted in same way aren't same?

3. Aug 1, 2015

### Staff: Mentor

As far as I can tell they are not the same equation.