Internal problem ID [7308]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 588.
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 (9 x^{2}+1\right ) y^{\prime }+\left (25 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 41
dsolve(x^2*(1+x^2)*diff(y(x),x$2)-x*(1+9*x^2)*diff(y(x),x)+(1+25*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \left (x^{4}-4 x^{2}+1\right )+c_{2} \left (\left (x^{4}-4 x^{2}+1\right ) \ln \relax (x )-6 x^{2}+3\right ) x \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 43
DSolve[x^2*(1+x^2)*y''[x]-x*(1+9*x^2)*y'[x]+(1+25*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x^5-4 x^3+x\right )+c_2 x \left (-6 x^2+\left (x^4-4 x^2+1\right ) \log (x)+3\right ) \\ \end{align*}