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

解

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

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

解答ステップ

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

代用

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

と

y^{''} (x)

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

解く

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

解く

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