29.5.4 problem 4

Internal problem ID [7273]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 5. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND ZERO RIGHT-HAND SIDE. page 414
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:27:40 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = {\mathrm e}^{-x} \left (c_1 \sin \left (x \right )+c_2 \cos \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to e^{-x} (c_2 \cos (x)+c_1 \sin (x)) \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{- x} \]