Internal problem ID [7504]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 787.
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: 0.003 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x^{2}}+c_{2} {\mathrm e}^{x^{2}} x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 18
DSolve[y''[x]-4*x*y'[x]+(4*x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2} (c_2 x+c_1) \\ \end{align*}