Internal problem ID [8625]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1047.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(4*x^2+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x^{2}} c_{1} +c_{2} {\mathrm e}^{-x^{2}} x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 20
DSolve[(2 + 4*x^2)*y[x] + 4*x*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x^2} (c_2 x+c_1) \\ \end{align*}