What is the solution for (3xy^2+x^3)y^'=3y^3+x^2y ?

The solution for (3xy^2+x^3)y^'=3y^3+x^2y is y=c_{1}x

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(3xy^2+x^3)y^'=3y^3+x^2y

(3 x y^{2} + x^{3}) y^{^{'}} = 3 y^{3} + x^{2} y

y = c_{1} x

Solution steps

(3 x y^{2} + x^{3}) y^{'} (x) = 3 y^{3} + x^{2} y

Solve separable ODE:

y = c_{1} x

y = c_{1} x

(3 y^{2} x^{2} - 3 x^{2}) d x + (5 x^{3} y) d y = 0

\frac{d y}{d x} = ln (x^{y}), y (1) = 1

(y^{2} + y) d x - x d y = 0, y (1) = 1

y^{^{'}} = - x^{5} y^{2}

\frac{d y}{d x} + \frac{y}{5} = y^{- 3}

What is the solution for (3xy^2+x^3)y^'=3y^3+x^2y ?
The solution for (3xy^2+x^3)y^'=3y^3+x^2y is y=c_{1}x