Internal problem ID [7256]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 536.
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 }-2 x \left (-x^{2}+2\right ) y^{\prime }+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(x^2*(1+x^2)*diff(y(x),x$2)-2*x*(2-x^2)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{4}}{\left (x^{2}+1\right )^{2}}+\frac {c_{2} \left (3 x^{3}+x \right )}{\left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 35
DSolve[x^2*(1+x^2)*y''[x]-2*x*(2-x^2)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {-3 c_1 x^4+3 c_2 x^3+c_2 x}{3 \left (x^2+1\right )^2} \\ \end{align*}