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

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

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

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

y = \frac{π}{4} c_{1} erf (x) + \frac{1}{2} x + c_{2}

Solution steps

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

Solve using substitution:

y = \frac{π}{4} c_{1} erf (x) + \frac{1}{2} x + c_{2}

y = \frac{π}{4} c_{1} erf (x) + \frac{1}{2} x + c_{2}

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