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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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