59.1.481 problem 497

Internal problem ID [9653]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 497
Date solved : Monday, January 27, 2025 at 06:05:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-8 x +14\right ) y^{\prime \prime }-8 \left (x -4\right ) y^{\prime }+20 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 55

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)
 

\[ y = c_{1} x^{5}+c_{2} x^{4}+4 \left (-35 c_{1} -4 c_{2} \right ) x^{3}+20 \left (56 c_{1} +5 c_{2} \right ) x^{2}+4 \left (-875 c_{1} -72 c_{2} \right ) x +4032 c_{1} +\frac {1604 c_{2}}{5} \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 77

DSolve[(x^2-8*x+14)*D[y[x],{x,2}]+8*(x-4)*D[y[x],x]+20*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1 P_{\frac {1}{2} i \left (i+\sqrt {31}\right )}^3\left (\frac {x-4}{\sqrt {2}}\right )+c_2 Q_{\frac {1}{2} i \left (i+\sqrt {31}\right )}^3\left (\frac {x-4}{\sqrt {2}}\right )}{\left (x^2-8 x+14\right )^{3/2}} \]