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

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

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y^'+2xy=e^x

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

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

Solution steps

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

Solve linear ODE:

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

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

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