59.1.61 problem 63

Internal problem ID [9233]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 63
Date solved : Sunday, March 30, 2025 at 02:26:11 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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 55

ode:=(x^2-8*x+14)*diff(diff(y(x),x),x)-8*(-4+x)*diff(y(x),x)+20*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{5}+c_2 \,x^{4}+4 \left (-35 c_1 -4 c_2 \right ) x^{3}+20 \left (56 c_1 +5 c_2 \right ) x^{2}+4 \left (-875 c_1 -72 c_2 \right ) x +4032 c_1 +\frac {1604 c_2}{5} \]

✓ Mathematica. Time used: 0.094 (sec). Leaf size: 77

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((32 - 8*x)*Derivative(y(x), x) + (x**2 - 8*x + 14)*Derivative(y(x), (x, 2)) + 20*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False