59.1.379 problem 388

Internal problem ID [9551]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 388
Date solved : Wednesday, March 05, 2025 at 07:50:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

ode:=x*diff(diff(y(x),x),x)+(1+x)*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 42

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

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

✗ Sympy

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

False