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

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

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

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

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

Solution steps

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

Solve using substitution:

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

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

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