Internal problem ID [9485]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1150.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve(x^2*diff(diff(y(x),x),x)+(x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (-\sin \left (x \right )+\cos \left (x \right ) x \right )}{x}+\frac {c_{2} \left (\cos \left (x \right )+x \sin \left (x \right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 21
DSolve[(-2 + x^2)*y[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_1 j_1(x)-c_2 y_1(x)) \]