59.1.73 problem 75

Internal problem ID [9245]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 75
Date solved : Wednesday, March 05, 2025 at 07:46:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-\left (6-7 x \right ) y^{\prime }+8 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 50

ode:=x^2*diff(diff(y(x),x),x)-(6-7*x)*diff(y(x),x)+8*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {108 c_{2} {\mathrm e}^{-\frac {6}{x}} \left (x -2\right ) \operatorname {Ei}_{1}\left (-\frac {6}{x}\right )+c_{1} {\mathrm e}^{-\frac {6}{x}} \left (x -2\right )+x c_{2} \left (x^{2}+12 x -36\right )}{x^{5}} \]

✓ Mathematica. Time used: 0.361 (sec). Leaf size: 55

ode=x^2*D[y[x],{x,2}]-(6-7*x)*D[y[x],x]+8*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{5-\frac {6}{x}} (x-2) \left (c_2 \int _1^x\frac {e^{\frac {6}{K[1]}-3} K[1]^3}{(K[1]-2)^2}dK[1]+c_1\right )}{x^5} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - (6 - 7*x)*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 2)) - 8*y(x))/(7*x - 6) cannot be solved by the factorable group method