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

The solution for (dy)/(dx)-yx-y^2=0 is y=(sqrt(2)e^{(x^2)/2})/(c_{1)-sqrt(pi)\erfi(x/(sqrt(2)))}

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(dy)/(dx)-yx-y^2=0

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

y = \frac{2 e ^{\frac{x ^{2}}{2}}}{c _{1} - π erfi ( \frac{x}{2} )}

Solution steps

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

Solve Bernoulli ODE:

y = \frac{2 e ^{\frac{x ^{2}}{2}}}{c _{1} - π erfi ( \frac{x}{2} )}

y = \frac{2 e ^{\frac{x ^{2}}{2}}}{c _{1} - π erfi ( \frac{x}{2} )}

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