Edit: Looks good to me.
But I did not check your partial fraction.
Could you please have a look at this and see if i have done it correctly? thanks!
Would you multiply the numerator and denominator by
And then given the substitution that
So then, putting both equations together,
Rearranging to give:
Then use partial fractions on the first integral:
then simply integrate, sub v in, then try to rearrange for y?
havan't gone homogeneous ODE's before, just trying one out with the method.