Internal problem ID [7569]
Book: Collection of Kovacic problems
Section: section 2. Solution found using all possible Kovacic cases
Problem number: 9.
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}+2\right ) y^{\prime \prime }-x \left (4 x^{2}+3\right ) y^{\prime }+\left (-2 x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.25 (sec). Leaf size: 47
dsolve(x^2*(2-x^2)*diff(y(x), x$2) - x*(3+4*x^2)*diff(y(x), x) + (2-2*x^2)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2} \hypergeom \left (\left [\frac {3}{2}, 2\right ], \left [\frac {7}{4}\right ], \frac {x^{2}}{2}\right )+\frac {c_{2} \sqrt {x}\, \left (x^{2}+1\right )}{\left (-2 x^{2}+4\right )^{\frac {3}{4}} \left (x^{2}-2\right )} \]
✓ Solution by Mathematica
Time used: 10.12 (sec). Leaf size: 86
DSolve[x^2*(2-x^2)*y''[x] - x*(3+4*x^2)*y'[x] + (2-2*x^2)*y[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2^{3/4} c_2 \left (x^2+1\right ) x^2 \, _2F_1\left (\frac {1}{4},\frac {3}{4};\frac {7}{4};\frac {x^2}{2}\right )+3 c_2 \left (2-x^2\right )^{3/4} x^2+6 c_1 \left (x^2+1\right ) \sqrt {x}}{6 \left (2-x^2\right )^{7/4}} \\ \end{align*}