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

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

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(dy)/(dx)=xy+y^2

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

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

Solution steps

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

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} )}

\int \frac{12 x ^{2}}{4 x ^{3} - 6} d x

y^{^{'}} = \frac{( 3 x sec ( \frac{y}{x} ) + y )}{x}

\frac{\partial}{\partial x} (\frac{x ^{2} - 2 y}{4 x ^{2} + 2 y})

\frac{\partial}{\partial y} (x y^{4})

f (x) = x^{3} - 3 x + 2, at x = 4

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