59.1.355 problem 362

Internal problem ID [9527]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 362
Date solved : Sunday, March 30, 2025 at 02:36:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

\[ y = c_1 \left (x -2\right )+c_2 \,{\mathrm e}^{-\frac {x}{2}} \]

✓ Mathematica. Time used: 0.291 (sec). Leaf size: 43

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

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

✗ Sympy

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

False