Internal problem ID [6892]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 160.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }-x \left (3 x^{2}+2\right ) y^{\prime }+\left (-x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(x^2*(2-x^2)*diff(y(x),x$2)-x*(2+3*x^2)*diff(y(x),x)+(2-x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{x^{2}-2}+\frac {c_{2} x \ln \relax (x )}{x^{2}-2} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 23
DSolve[x^2*(2-x^2)*y''[x]-x*(2+3*x^2)*y'[x]+(2-x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x (c_2 \log (x)+c_1)}{x^2-2} \\ \end{align*}