Internal problem ID [7196]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 475.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+\left (x^{2}+2 x +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)-2*x*(x+1)*diff(y(x),x)+(x^2+2*x+2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} c_{1} x +c_{2} {\mathrm e}^{x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 41
DSolve[x^2*y''[x]-2*x*y'[x]+(x^2+2*x+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{i x} x (c_1 \operatorname {HypergeometricU}(-i,0,-2 i x)+c_2 L_i^{-1}(-2 i x)) \\ \end{align*}