Internal problem ID [6826]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 94.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (3+x \right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+\left (x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.218 (sec). Leaf size: 36
dsolve(2*x^2*(3+x)*diff(y(x),x$2)+x*(1+5*x)*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \hypergeom \left (\left [1, \frac {3}{2}\right ], \left [\frac {7}{6}\right ], -\frac {x}{3}\right )+\frac {c_{2} x^{\frac {1}{3}}}{\left (3+x \right ) \left (1+\frac {x}{3}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 10.042 (sec). Leaf size: 50
DSolve[2*x^2*(3+x)*y''[x]+x*(1+5*x)*y'[x]+(1+x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{x} \left (6 \sqrt [3]{3} c_2 \sqrt [6]{x} \, _2F_1\left (-\frac {1}{3},\frac {1}{6};\frac {7}{6};-\frac {x}{3}\right )+c_1\right )}{(x+3)^{4/3}} \\ \end{align*}