Internal problem ID [7209]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 488.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }+20 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve((1+x^2)*diff(y(x),x$2)-8*x*diff(y(x),x)+20*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (5 x^{4}-10 x^{2}+1\right )+c_{2} \left (x^{5}-10 x^{3}+5 x \right ) \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 38
DSolve[(1+x^2)*y''[x]-8*x*y'[x]+20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} i c_2 \left (5 \left (x^2-2\right ) x^2+1\right )+c_1 (1+i x)^5 \\ \end{align*}