Internal problem ID [6795]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 63.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 45
dsolve((x^2-8*x+14)*diff(y(x),x$2)-8*(x-4)*diff(y(x),x)+20*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{5}-140 x^{3}+1120 x^{2}-3500 x +4032\right )+c_{2} \left (\frac {1604}{5}+x^{4}-16 x^{3}+100 x^{2}-288 x \right ) \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 76
DSolve[(x^2-8*x+14)*y''[x]+8*(x-4)*y'[x]+20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 P_{\frac {1}{2} i \left (i+\sqrt {31}\right )}^3\left (\frac {x-4}{\sqrt {2}}\right )+c_2 Q_{\frac {1}{2} i \left (i+\sqrt {31}\right )}^3\left (\frac {x-4}{\sqrt {2}}\right )}{((x-8) x+14)^{3/2}} \\ \end{align*}