What is the solution for (2xy^4+2xy^2)dx+(x^2y^3+x^2y)dy=0 ?

The solution for (2xy^4+2xy^2)dx+(x^2y^3+x^2y)dy=0 is y=(c_{1})/(x^2)

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(2xy^4+2xy^2)dx+(x^2y^3+x^2y)dy=0

(2 x y^{4} + 2 x y^{2}) d x + (x^{2} y^{3} + x^{2} y) d y = 0

y = \frac{c _{1}}{x ^{2}}

Solution steps

(2 x y^{4} + 2 x y^{2}) d x + (x^{2} y^{3} + x^{2} y) d y = 0

Solve separable ODE:

y = \frac{c _{1}}{x ^{2}}

y = \frac{c _{1}}{x ^{2}}

(1 + y^{2}) d x = (y - 1 + y^{2}) (1 + x^{2})^{\frac{3}{2}} d y

\frac{d y}{d t} = 5 + 5 y + t + t y, y (0) = 3

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

x + y \frac{d y}{d x} = 0

x^{^{'}} + 2 x = 0

What is the solution for (2xy^4+2xy^2)dx+(x^2y^3+x^2y)dy=0 ?
The solution for (2xy^4+2xy^2)dx+(x^2y^3+x^2y)dy=0 is y=(c_{1})/(x^2)