Internal problem ID [7033]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 302.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 x y^{\prime }+y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)+x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \cos \relax (x )+c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 39
DSolve[y''[x]-2*x*y'[x]+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{\frac {1}{2} x (x-2 i)} \left (2 c_1-i c_2 e^{2 i x}\right ) \\ \end{align*}