Internal problem ID [6837]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 105.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.182 (sec). Leaf size: 35
dsolve(3*x^2*(2-x^2)*diff(y(x),x$2)+x*(1-11*x^2)*diff(y(x),x)+(1-5*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{\left (-2 x^{2}+4\right )^{\frac {3}{4}}}+c_{2} x^{\frac {1}{3}} \hypergeom \left (\left [\frac {2}{3}, 1\right ], \left [\frac {11}{12}\right ], \frac {x^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 10.041 (sec). Leaf size: 57
DSolve[3*x^2*(2-x^2)*y''[x]+x*(1-11*x^2)*y'[x]+(1-5*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \sqrt {x}-3\operatorname {\ }2^{3/4} c_2 \sqrt [3]{x} \, _2F_1\left (-\frac {1}{12},\frac {1}{4};\frac {11}{12};\frac {x^2}{2}\right )}{\left (2-x^2\right )^{3/4}} \\ \end{align*}