Internal problem ID [6784]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 52.
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 }+6 x y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve((1+x^2)*diff(y(x),x$2)+6*x*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{\left (x^{2}+1\right )^{2}}+\frac {c_{2} \left (x^{2}-1\right )}{\left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 29
DSolve[(1+x^2)*y''[x]+6*x*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x-c_1 (x-i)^2}{\left (x^2+1\right )^2} \\ \end{align*}