I was told to solve this without integration and to use implicit diffentiation.
$$x^3 y^{\prime} - \dfrac{3y}{x} = x^3 e^{\left(x - \dfrac{1}{x^3}\right)}$$
I am utterly lost, any suggestions.
I can get to
$$ x^4y^{\prime} - 3y = x^4 e^{\left(x - \dfrac{1}{x^3}\right)}$$