Internal problem ID [7345]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 625.
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}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve(x^2*(1+x^2)*diff(y(x),x$2)-x*(5-x^2)*diff(y(x),x)-(7+25*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x \left (x^{2}+1\right )^{2}}+\frac {c_{2} x^{7} \left (4 x^{2}+5\right )}{\left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 37
DSolve[x^2*(1+x^2)*y''[x]-x*(5-x^2)*y'[x]-(7+25*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \left (4 x^2+5\right ) x^8+40 c_1}{40 x \left (x^2+1\right )^2} \\ \end{align*}