Internal problem ID [7874]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 391.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x^{2}+4 y^{\prime } x +\left (x^{2}+2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x^2*diff(y(x), x, x) + 4*x*diff(y(x), x) + (x^2+2)*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sin \left (x \right )}{x^{2}}+\frac {c_{2} \cos \left (x \right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 37
DSolve[x^2*y''[x]+4*x*y'[x]+(x^2+2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 c_1 e^{-i x}-i c_2 e^{i x}}{2 x^2} \]