What is the solution for y^'=2xy+1 ?

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

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y^'=2xy+1

y^{^{'}} = 2 x y + 1

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

Solution steps

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

Solve linear ODE:

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

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

\frac{y ^{^{'}}}{t + 3 y} = 3

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

f (x) = 5 x - 6

x \to 0 lim (\frac{( e ^{5 x} - 1 - 5 x )}{( x ^{2} )})

- \frac{d}{d x} y = \frac{4}{x}

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