What is the solution for v^2y^2dy+vy^3dv+2v^2y^2dy+y^2dy=0 ?

The solution for v^2y^2dy+vy^3dv+2v^2y^2dy+y^2dy=0 is y=(c_{1})/(\sqrt[6]{3v^2+1)}

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v^2y^2dy+vy^3dv+2v^2y^2dy+y^2dy=0

v^{2} y^{2} d y + v y^{3} d v + 2 v^{2} y^{2} d y + y^{2} d y = 0

Solution steps

v^{2} y^{2} d y + v y^{3} d v + 2 v^{2} y^{2} d y + y^{2} d y = 0

Solve separable ODE:

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

\frac{d x}{d y} = e^{2 x + 3 y}

(x y - 2 x + 4 y - 8) d y = (x y + 3 x - y - 3) d x

y^{^{'}} + 5 y = 20

y^{^{'}} = y^{2} (x + 1)

What is the solution for v^2y^2dy+vy^3dv+2v^2y^2dy+y^2dy=0 ?
The solution for v^2y^2dy+vy^3dv+2v^2y^2dy+y^2dy=0 is y=(c_{1})/(\sqrt[6]{3v^2+1)}