Internal problem ID [8754]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1176.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+(x^2+2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \sin \left (x \right )+c_{2} \cos \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 33
DSolve[(2 + x^2)*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-i x} x-\frac {1}{2} i c_2 e^{i x} x \\ \end{align*}