Internal problem ID [6899]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 167.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }+x \left (8-9 x \right ) y^{\prime }+\left (6-3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 42
dsolve(x^2*(1-2*x)*diff(y(x),x$2)+x*(8-9*x)*diff(y(x),x)+(6-3*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (3 x +4\right ) \left (2 x -1\right )^{\frac {9}{2}}}{x^{6}}+\frac {c_{2} \left (231 x^{3}-198 x^{2}+66 x -8\right )}{x^{6}} \]
✓ Solution by Mathematica
Time used: 0.165 (sec). Leaf size: 48
DSolve[x^2*(1-2*x)*y''[x]+x*(8-9*x)*y'[x]+(6-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {385 c_1 (3 x+4) (1-2 x)^{9/2}+c_2 (33 x (x (7 x-6)+2)-8)}{1155 x^6} \\ \end{align*}