Answer to Question #244279 in Differential Equations for Jac

Question

Solve the differential equation of the following homogeneous equation. Show complete solution.

(3x^2 y - 6x)dx + (x^3 + 2y)dy = 0

Answer 1

$d(x^3y-3x^2+y^2)=0;\\ x^3\cdot y-3x^2+y^2=C;\\ y^2+x^3\cdot y-3x^2-C=0;\\ y_{1,2}=\frac{-x^3\pm \sqrt{x^6+12x^4+C}}{2},\space C\in R$