What is the solution for (d^2y)/(dx^2)-2x(dy)/(dx)+2y=0 ?

The solution for (d^2y)/(dx^2)-2x(dy)/(dx)+2y=0 is y=-c_{1}e^{x^2}+sqrt(pi)\erfi(x)c_{1}x+c_{2}x

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(d^2y)/(dx^2)-2x(dy)/(dx)+2y=0

\frac{d ^{2} y}{d x ^{2}} - 2 x \frac{d y}{d x} + 2 y = 0

y = - c_{1} e^{x^{2}} + π erfi (x) c_{1} x + c_{2} x

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 x \frac{d y}{d x} + 2 y = 0

Solve using substitution:

y = - c_{1} e^{x^{2}} + π erfi (x) c_{1} x + c_{2} x

y = - c_{1} e^{x^{2}} + π erfi (x) c_{1} x + c_{2} x

What is the solution for (d^2y)/(dx^2)-2x(dy)/(dx)+2y=0 ?
The solution for (d^2y)/(dx^2)-2x(dy)/(dx)+2y=0 is y=-c_{1}e^{x^2}+sqrt(pi)\erfi(x)c_{1}x+c_{2}x