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}}}

\int x^{2} + 9 d x

x \to - 6 lim (x + 1)

x \to - 1 lim (x + x^{2} + x^{3})

\int \frac{1}{y ^{2} 5 - y ^{2}} d y

\frac{d}{d x} (\frac{x sin ( x )}{1 + cos ( x )})

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)}