What is the solution for (dy}{dx}=\frac{(xy^2-x))/y ?

The solution for (dy}{dx}=\frac{(xy^2-x))/y is y=sqrt(e^{x^2+c_{1)}+1},y=-sqrt(e^{x^2+c_{1)}+1}

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(dy}{dx}=\frac{(xy^2-x))/y

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{2 x}{e ^{2 y}}

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

\frac{d y}{y} = \frac{d x}{( x - 9 ) ^{2} - 5 ^{2}}

y^{^{'}} = - \frac{0.1 y}{0.5 - 0.025 x}

4 y^{11} + y^{^{'}} = 0

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