What is the solution for y^'=y(y+1)x ?

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

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y^'=y(y+1)x

y^{^{'}} = y (y + 1) x

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

Solution steps

y^{'} (x) = y (y + 1) x

Solve separable ODE:

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

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

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