Internal problem ID [8587]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1007.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(diff(y(x),x),x)-2*y(x)-4*x^2*exp(x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\sqrt {2}\, x} c_{2}+{\mathrm e}^{-\sqrt {2}\, x} c_{1}+{\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 36
DSolve[-4*E^x^2*x^2 - 2*y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2}+c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x} \\ \end{align*}