What is the solution for (d^2y)/(dx^2)=e^{5x^2} ?

The solution for (d^2y)/(dx^2)=e^{5x^2} is y=integral of (sqrt(pi))/(2sqrt(5))\erfi(sqrt(5)x)+c_{1}

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(d^2y)/(dx^2)=e^{5x^2}

\frac{d ^{2} y}{d x ^{2}} = e^{5 x^{2}}

y = \int \frac{π}{2 5} erfi (5 x) + c_{1} d x

Solution steps

\frac{d ^{2} y}{d x ^{2}} = e^{5 x^{2}}

Substitute

\frac{d ^{2} y}{d x ^{2}}

with

y^{''} (x)

y^{^{''}} (x) = e^{5 x^{2}}

Solve

y^{''} (x) = e^{5 x^{2}} : y^{'} (x) = \frac{π}{2 5} erfi (5 x) + c_{1}

Solve

y^{'} (x) = \frac{π}{2 5} erfi (5 x) + c_{1} : y = \int \frac{π}{2 5} erfi (5 x) + c_{1} d x

y = \int \frac{π}{2 5} erfi (5 x) + c_{1} d x

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What is the solution for (d^2y)/(dx^2)=e^{5x^2} ?
The solution for (d^2y)/(dx^2)=e^{5x^2} is y=integral of (sqrt(pi))/(2sqrt(5))\erfi(sqrt(5)x)+c_{1}