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

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

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

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

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

Solution steps

x \cdot \frac{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}}

x^{2}, 0, 1

n = 0 \sum \infty (- 1)^{n} x (\frac{x}{4})^{2 n}

\frac{d}{d x} (arctan (1 + x^{2}))

y = sin (sin (sin (x)))

x \to 5 lim (x 29 - x^{2})

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