Internal problem ID [6964]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 233.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {3 x^{2} y^{\prime \prime }-x \left (x +8\right ) y^{\prime }+6 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 31
dsolve(3*x^2*diff(y(x),x$2)-x*(x+8)*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\relax [3], \left [\frac {10}{3}\right ], \frac {x}{3}\right ) x^{3}+c_{2} \hypergeom \left (\left [\frac {2}{3}\right ], \left [-\frac {4}{3}\right ], \frac {x}{3}\right ) x^{\frac {2}{3}} \]
✓ Solution by Mathematica
Time used: 0.658 (sec). Leaf size: 62
DSolve[3*x^2*y''[x]-x*(x+8)*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{18} e^{x/3} x^{2/3} ((x-2) x+4) \left (18 c_1-\sqrt [3]{3} c_2 \text {Gamma}\left (\frac {1}{3},\frac {x}{3}\right )\right )+\frac {1}{6} c_2 (x-4) x \\ \end{align*}