Internal problem ID [6719]
Book: Second order enumerated odes
Section: section 2
Problem number: 34.
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 y^{\prime }+2 \left (x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)+2*(1+x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \sin \left (x \sqrt {2}\right )+c_{2} x \cos \left (x \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 48
DSolve[x^2*y''[x]-2*x*y'[x]+2*(1+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-i \sqrt {2} x} x-\frac {i c_2 e^{i \sqrt {2} x} x}{2 \sqrt {2}} \\ \end{align*}