59.1.71 problem 73

Internal problem ID [9243]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 73
Date solved : Wednesday, March 05, 2025 at 07:46:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (4+x \right ) y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 53

ode:=(x+4)*diff(diff(y(x),x),x)+(x+2)*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x -4} c_{2} x \left (x +4\right )^{3} \operatorname {Ei}_{1}\left (-x -4\right )+c_{1} {\mathrm e}^{-x} x \left (x +4\right )^{3}+c_{2} \left (x^{3}+9 x^{2}+22 x +6\right ) \]

✓ Mathematica. Time used: 0.375 (sec). Leaf size: 93

ode=(4+x)*D[y[x],{x,2}]+(2+x)*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \exp \left (\int _1^x-\frac {K[1]}{2 (K[1]+4)}dK[1]-\frac {1}{2} \int _1^x\frac {K[2]+2}{K[2]+4}dK[2]\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[3]}-\frac {K[1]}{2 (K[1]+4)}dK[1]\right )}{K[3]^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2)*Derivative(y(x), x) + (x + 4)*Derivative(y(x), (x, 2)) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False