Internal problem ID [6900]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 168.
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 (10 x^{2}+3\right ) y^{\prime }-\left (-14 x^{2}+15\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.82 (sec). Leaf size: 66
dsolve(x^2*(1+x^2)*diff(y(x),x$2)+x*(3+10*x^2)*diff(y(x),x)-(15-14*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{3}}{\left (x^{2}+1\right )^{\frac {5}{2}}}+\frac {c_{2} \left (\arctanh \left (\frac {1}{\sqrt {x^{2}+1}}\right ) x^{8}-\left (x^{4}-\frac {8}{3} x^{2}-\frac {8}{3}\right ) \sqrt {x^{2}+1}\, \left (x^{2}+2\right )\right )}{\left (x^{2}+1\right )^{\frac {5}{2}} x^{5}} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 75
DSolve[x^2*(1+x^2)*y''[x]+x*(3+10*x^2)*y'[x]-(15-14*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {128 c_1 x^8+c_2 \left (\sqrt {x^2+1} \left (x^2+2\right ) \left (3 x^4-8 x^2-8\right )-3 x^8 \tanh ^{-1}\left (\sqrt {x^2+1}\right )\right )}{128 x^5 \left (x^2+1\right )^{5/2}} \\ \end{align*}