Internal problem ID [6840]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 108.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+5 x \left (6 x^{2}+1\right ) y^{\prime }-\left (-40 x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 35
dsolve(2*x^2*(1+2*x^2)*diff(y(x),x$2)+5*x*(1+6*x^2)*diff(y(x),x)-(2-40*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{\left (2 x^{2}+1\right )^{\frac {3}{2}}}+\frac {c_{2} \hypergeom \left (\left [\frac {1}{4}, 1\right ], \left [-\frac {1}{4}\right ], -2 x^{2}\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 10.073 (sec). Leaf size: 52
DSolve[2*x^2*(1+2*x^2)*y''[x]+5*x*(1+6*x^2)*y'[x]-(2-40*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {5 c_1 x^{5/2}-2 c_2 \, _2F_1\left (-\frac {5}{4},-\frac {1}{2};-\frac {1}{4};-2 x^2\right )}{5 x^2 \left (2 x^2+1\right )^{3/2}} \\ \end{align*}