How to find solution to differential equation

Question

Find the general solution to the differential equation (dy/dx)=6-x²(dy/dx). 

The steps I would usually take is isolate dy/dx and then find the antiderivative which I would then add C to since it asked for general. The part I am stuck on is how to isolate dy/dx when it is multiplying x²?

Answer 1

let dy/dx = y' Then y'=6-x²y' and y'+x²y'=6, factor y' out, y'(1+x²)=6, y'=6/(1+x²), dy = (1+x²) dx

 

Take integral of both sides, ∫dy = ∫(6/(1+x²) dx , y = 6∫(1/(x²+1) dx = 6 tan^-1 x + C , or 6 arctan x + C