Internal problem ID [8221]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 746.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime } x +x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )+c_{2} {\mathrm e}^{\frac {x^{2}}{2}} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 39
DSolve[y''[x]-2*x*y'[x]+x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{\frac {1}{2} x (x-2 i)} \left (2 c_1-i c_2 e^{2 i x}\right ) \]