Trying to obtain an explicit solution of a second order ODE

Hopefully this will appear in the right thread:

Aleksas,

thanks a lot for the answer. There was a small mistake in my ODE: the
correct one is

de: 'diff(y,x,2)=C*'diff(y,x)^2/y;

where C is positive, as before. I tried following again your steps, and
this time solve gives me back

(%o5) [y=%k1*y^C*(x*(1-C)+%k2*(1-C))]

This is basically ok: I just wonder why Maxima doesn't divide first and
second member by y^C. This doesn't seem to be related to the possibility of
y being 0, since adding

assume(y>0);

doesn't change the result. Anyway, this was enough to check that my manual
solution was correct (and that the one usually found in papers and books is
incomplete :) Thanks a lot,

Best Regards

deltaquattro



2013/4/17 <deltaquattro at gmail.com>

> Hi, all,
>
> I have the following ODE:
>
> assume(C>0);
>
> de: 'diff(y,x,2)=-C*'diff(y,x)^2/y;
>
> ode2 solves it easily:
>
> ode2(de,y,x);
>
> (%o5) (y*%e^(log(y)*C))/(%k1*C+%k1)=x+%k2
>
> I would like to get an explicit solution, in order to check my own
> explicit solution found by hand. How can I do that? Thanks,
>
> best regards
>
> deltaquattro
>