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

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

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e^x(dy)/(dx)-y^2(x+1)=0

e^{x} \frac{d y}{d x} - y^{2} (x + 1) = 0

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

Solution steps

e^{x} \frac{d y}{d x} - y^{2} (x + 1) = 0

Solve separable ODE:

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

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

\frac{d y}{d x} 2 x^{3} y + 3 x y^{3} = 0

(\frac{x}{x ^{2} + y ^{2}}) d x - (\frac{y}{x ^{2} + y ^{2}}) d y = 0

y^{^{'}} = \frac{2}{3 x y + y}

x y \cdot y^{^{'}} = y - 1

x e^{x^{2}} + y y^{^{'}} = 0, y (0) = 1

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