Internal problem ID [7961]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 484.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (1-x^{2}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 59
dsolve(x^2*(1+2*x^2)*diff(y(x),x$2)+x*(4+2*x^2)*diff(y(x),x)+2*(1-x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+\frac {c_{2} \sqrt {2}\, \left (\sqrt {2}\, \sqrt {2 x^{2}+1}\, x^{2}+3 \,\operatorname {arcsinh}\left (\sqrt {2}\, x \right ) x -\sqrt {2}\, \sqrt {2 x^{2}+1}\right )}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 77
DSolve[x^2*(1+2*x^2)*y''[x]+x*(4+2*x^2)*y'[x]+2*(1-x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {c_2 \sqrt {2 x^2+1}}{x^2}+c_2 \sqrt {2 x^2+1}-\frac {3 c_2 \log \left (\sqrt {2 x^2+1}-\sqrt {2} x\right )}{\sqrt {2} x}+\frac {c_1}{x} \]