Internal problem ID [8015]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 539.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+x \left (-11 x^{2}+1\right ) y^{\prime }+\left (-5 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
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)
\[ y \left (x \right ) = \frac {c_{1} \sqrt {x}}{\left (x^{2}-2\right )^{\frac {3}{4}}}+\frac {c_{2} \sqrt {x}\, \left (\int \frac {1}{\left (x^{2}-2\right )^{\frac {1}{4}} x^{\frac {7}{6}}}d x \right )}{\left (x^{2}-2\right )^{\frac {3}{4}}} \]
✓ Solution by Mathematica
Time used: 0.095 (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]
\[ y(x)\to \frac {c_1 \sqrt {x}-3\ 2^{3/4} c_2 \sqrt [3]{x} \operatorname {Hypergeometric2F1}\left (-\frac {1}{12},\frac {1}{4},\frac {11}{12},\frac {x^2}{2}\right )}{\left (2-x^2\right )^{3/4}} \]