59.1.727 problem 744

Internal problem ID [9899]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 744
Date solved : Wednesday, March 05, 2025 at 08:00:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+x y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.226 (sec). Leaf size: 40

ode=x*D[y[x],{x,2}]+x*D[y[x],x]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

False