Internal problem ID [7215]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 495.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve((11-8*x+2*x^2)*diff(y(x),x$2)-16*(x-2)*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-\frac {31}{5}+x^{3}-6 x^{2}+\frac {111}{10} x \right )+c_{2} \left (x^{6}-12 x^{5}+\frac {165}{2} x^{4}-\frac {16577}{8}-\frac {5445}{4} x^{2}+3267 x \right ) \]
✓ Solution by Mathematica
Time used: 0.742 (sec). Leaf size: 87
DSolve[(11-8*x+2*x^2)*y''[x]-16*(x-2)*y'[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 \left (2 x+5 i \sqrt {6}-4\right ) (2 (x-4) x+11)^2 \left (2 i x+\sqrt {6}-4 i\right )^3}{2 \left (-2 i x+\sqrt {6}+4 i\right )^2}+\frac {1}{15} i c_2 (x-2) (10 (x-4) x+31) \\ \end{align*}