What is the solution for (x^3+xy^2)dx+(x^2y+y^3)dy=0 ?

The solution for (x^3+xy^2)dx+(x^2y+y^3)dy=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}

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

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

y = - x^{2} + c_{1}, y = - - x^{2} + c_{1}

Solution steps

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

Solve separable ODE:

y = - x^{2} + c_{1}, y = - - x^{2} + c_{1}

y = - x^{2} + c_{1}, y = - - x^{2} + c_{1}

\frac{d x}{d t} = 50 - \frac{x}{100}

\frac{d z}{d t} + 6 e^{t + z} = 0

y^{^{'}} = y y^{2} - 1

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

\frac{d y}{d x} - \frac{y}{3 x - 1} = 0

What is the solution for (x^3+xy^2)dx+(x^2y+y^3)dy=0 ?
The solution for (x^3+xy^2)dx+(x^2y+y^3)dy=0 is y=sqrt(-x^2+c_{1)},y=-sqrt(-x^2+c_{1)}