Internal problem ID [7343]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 623.
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 (11 x^{2}+5\right ) y^{\prime }+24 y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(x^2*(1+x^2)*diff(y(x),x$2)+x*(5+11*x^2)*diff(y(x),x)+24*x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\left (x^{2}+1\right )^{2}}+\frac {c_{2} \left (2 x^{2}+1\right )}{x^{4} \left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 36
DSolve[x^2*(1+x^2)*y''[x]+x*(5+11*x^2)*y'[x]+24*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-4 c_1 x^4+2 c_2 x^2+c_2}{4 x^4 \left (x^2+1\right )^2} \\ \end{align*}