54.3.122 problem 1136

Internal problem ID [12417]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1136
Date solved : Wednesday, October 01, 2025 at 01:44:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

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

\[ y = {\mathrm e}^{\frac {x}{2}} \left (c_2 \,\operatorname {Ei}_{1}\left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 41

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

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

✗ Sympy

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

False