Internal problem ID [8630]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1050.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(diff(y(x),x),x)-4*x*diff(y(x),x)+(4*x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2}} c_{1}+c_{2} {\mathrm e}^{x^{2}} x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 18
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*}