$xy^n + 2\frac{dy}{dx} = 12x^2$
Solve the second-order differential equation by making the substitution $u = \frac{dy}{dx} $
this is the question.
I tried to solve it using the integration factor. But since it has a $y^n$ in i can't figure it out.
They do say solve the second order differential equation does this mean that since it is second order that $y$ should equeal $2$? Should i use the integration factor or use a different technique? I also dont get how substituting $u$ for $\frac{dy}{dx}$ would do anything.
There are several indication that the original problem was $$ xy''+2y'=12x^2, $$ not the least because then the factor $12$ allows for a "nice" (with simple coefficients/constants) solution $$ y=x^3+\frac{c}x+d. $$
At some point the superscript in $y''$ was mis-interpreted as the similar looking $n$.