What is the solution for (xdy)/(dx)-(1+x)y=xy^2 ?

The solution for (xdy)/(dx)-(1+x)y=xy^2 is y=(xe^x)/(-e^xx+e^x+c_{1)}

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(xdy)/(dx)-(1+x)y=xy^2

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

y = \frac{x e ^{x}}{- e ^{x} x + e ^{x} + c _{1}}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{x e ^{x}}{- e ^{x} x + e ^{x} + c _{1}}

y = \frac{x e ^{x}}{- e ^{x} x + e ^{x} + c _{1}}

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