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

The solution for y^'+2xy=x^2 is y= x/2-(sqrt(pi)\erfi(x))/(4e^{x^2)}+(c_{1})/(e^{x^2)}

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y^'+2xy=x^2

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

y = \frac{x}{2} - \frac{π erfi ( x )}{4 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}}}

Solution steps

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

Solve linear ODE:

y = \frac{x}{2} - \frac{π erfi ( x )}{4 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}}}

y = \frac{x}{2} - \frac{π erfi ( x )}{4 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}}}

f (x) = \frac{4 x ^{3} - 2 x + 1}{x ^{2}}

x \to + 6 lim (3)

\int x (1 - x)^{2} d x

x \to - 2 lim (x^{2} + 5 x + 4)

\int \frac{x + 2}{x + 1} d x

What is the solution for y^'+2xy=x^2 ?
The solution for y^'+2xy=x^2 is y= x/2-(sqrt(pi)\erfi(x))/(4e^{x^2)}+(c_{1})/(e^{x^2)}