59.1.352 problem 359

Internal problem ID [9524]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 359
Date solved : Sunday, March 30, 2025 at 02:36:47 PM
CAS classification : [_Laguerre]

\begin{align*} x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

ode:=x*diff(diff(y(x),x),x)-(1+x)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,{\mathrm e}^{x}+c_1 x +c_1 \]

✓ Mathematica. Time used: 0.4 (sec). Leaf size: 78

ode=x*D[y[x],{x,2}]-(x+1)*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - (x + 1)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False