# Math Help - Homogeneous ODE

1. ## Homogeneous ODE

Thanks...

I got this homogeneous equation:

(2.r - s)ds + (r - 2.s)dr = 0

y = 2+s
x = r-1

t = r/s
dr = s.dt + t.ds

And got this:

ds/s = (2-t).dt/t²-1

The integration leads me to a complicated and large answer, is there any better options here?

2. ## Re: Homogeneous ODE

Originally Posted by mafra
And got this: ds/s = (2-t).dt/t²-1 . The integration leads me to a complicated and large answer, is there any better options here?
I don't know why do you say that is a complicated and large answer. With a similar substitution $s=vr$ , I get $\log |r|+\int \frac{2-v}{1-v^2}dv=C$ i.e., a simple integral.