82.40.3 problem Ex. 3

Internal problem ID [18878]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 94
Problem number : Ex. 3
Date solved : Monday, March 31, 2025 at 06:17:58 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x y^{\prime \prime }+2 x y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 34

ode=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]
 

\[ y(x)\to e^{-2 x} \left (2 c_2 x \operatorname {ExpIntegralEi}(2 x)+c_1 x-c_2 e^{2 x}\right ) \]

✗ Sympy

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

False