Internal problem ID [8011]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 535.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {8 x^{2} \left (1-x^{2}\right ) y^{\prime \prime }+2 x \left (-13 x^{2}+1\right ) y^{\prime }+\left (-9 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 60
dsolve(8*x^2*(1-x^2)*diff(y(x),x$2)+2*x*(1-13*x^2)*diff(y(x),x)+(1-9*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {\frac {1}{\left (x -1\right ) \left (x +1\right )}}\, x^{\frac {1}{4}}+c_{2} \sqrt {\frac {1}{\left (x -1\right ) \left (x +1\right )}}\, x^{\frac {1}{4}} \left (\int \frac {\sqrt {\frac {1}{\left (x -1\right ) \left (x +1\right )}}}{x^{\frac {3}{4}}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 47
DSolve[8*x^2*(1-x^2)*y''[x]+2*x*(1-13*x^2)*y'[x]+(1-9*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [4]{x} \left (4 c_2 \sqrt [4]{x} \operatorname {Hypergeometric2F1}\left (\frac {1}{8},\frac {1}{2},\frac {9}{8},x^2\right )+c_1\right )}{\sqrt {1-x^2}} \]