What is the solution for (4x^2y^2-x^2+4xy^2-x)dx+(2xy+x+2y+1)dy=0 ?

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

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(4x^2y^2-x^2+4xy^2-x)dx+(2xy+x+2y+1)dy=0

(4 x^{2} y^{2} - x^{2} + 4 x y^{2} - x) d x + (2 x y + x + 2 y + 1) d y = 0

y = \frac{e ^{- x^{2} + c_{1}}}{2} + \frac{1}{2}

Solution steps

(4 x^{2} y^{2} - x^{2} + 4 x y^{2} - x) d x + (2 x y + x + 2 y + 1) d y = 0

Solve separable ODE:

y = \frac{e ^{- x^{2} + c_{1}}}{2} + \frac{1}{2}

y = \frac{e ^{- x^{2} + c_{1}}}{2} + \frac{1}{2}

\frac{d y}{d x} = \frac{3 y}{x ^{6}}

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

\frac{d y}{- y + 10} = \frac{d x}{x + 1}

x y^{^{'}} - y = 2 x^{3} y

\frac{d y}{d t} = \frac{t + 1}{t y}, y (1) = - 3

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