Internal problem ID [7592]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 104.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} \left (1-x^{2}\right ) y^{\prime \prime }+x \left (-19 x^{2}+7\right ) y^{\prime }-\left (14 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 60
dsolve(4*x^2*(1-x^2)*diff(y(x),x$2)+x*(7-19*x^2)*diff(y(x),x)-(1+14*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \sqrt {\frac {1}{\left (x -1\right ) \left (x +1\right )}}}{x}+\frac {c_{2} \sqrt {\frac {1}{\left (x -1\right ) \left (x +1\right )}}\, \left (\int \sqrt {\frac {1}{\left (x -1\right ) \left (x +1\right )}}\, x^{\frac {1}{4}}d x \right )}{x} \]
✓ Solution by Mathematica
Time used: 20.113 (sec). Leaf size: 50
DSolve[4*x^2*(1-x^2)*y''[x]+x*(7-19*x^2)*y'[x]-(1+14*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 c_2 x^{5/4} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {5}{8},\frac {13}{8},x^2\right )+5 c_1}{5 x \sqrt {1-x^2}} \]