7.8.9 problem 9

Internal problem ID [223]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 9
Date solved : Tuesday, March 04, 2025 at 11:05:32 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.016 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 0; 
ic:=y(0) = 2, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (x +2\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

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

\[ y(x)\to 2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right ) \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 8

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

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