this is a question that's had me sort of stumped. Any points or help would be greatly appreciated, I've never been that great at differential equations
The presence of the alpha seems to throw off any actual working I do such as manipulating for a value of y prime, and I'd rather use an integration factor but the change of variables has been specified for? I also can't seem to find any change of variable questions similar enough to follow the working. Thanks in advance to whoever helps out.
$$y'-2xy=\dfrac {x^3}{y^3}$$ This is Bernoulli's differential equation. $$y^3y'-2xy^4=x^3$$ Note that $(y^4)'=4y^3y'$. Substitute $v=y^4$ and solve.
You can surely take it from here.