Internal problem ID [6925]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 193.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.13 (sec). Leaf size: 29
dsolve(4*x^2*(1+x^2)*diff(y(x),x$2)+4*x*(2+x^2)*diff(y(x),x)-(15+x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (3 x^{2}+2\right )}{x^{\frac {5}{2}}}+\frac {c_{2} \left (x^{2}+1\right )^{\frac {3}{2}}}{x^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 39
DSolve[4*x^2*(1+x^2)*y''[x]+4*x*(2+x^2)*y'[x]-(15+x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_1 \left (x^2+1\right )^{3/2}-c_2 \left (3 x^2+2\right )}{3 x^{5/2}} \\ \end{align*}