I was solving ODE $x^5yy'+y^4x^2-xy^5=0 $ with condition $y\left(2\right)=1$. Since it is homogeneous equation i substitute $y=vx$ and calculate furthur but i stuck at integration which is $\int\dfrac{1}{v^4-v^3-v}dv.$
$\int\dfrac{1}{v^4-v^3-v}dv=\int \dfrac{1}{v\left(v^3-v^2-1\right)}dv.$
Then i did partial fraction and i get $\dfrac{-1}{v}+\dfrac{v^2-v}{v^3-v-1}$. I don't know how to deal with second. (I am not sure i did correcr partial fraction).
Any hint how to integrate. Thank you.