58.10.29 problem 29

Internal problem ID [14716]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 29
Date solved : Thursday, October 02, 2025 at 09:50:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+9*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} \left (2+3 x \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 16

ode=D[y[x],{x,2}]+6*D[y[x],x]+9*y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} (3 x+2) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (3 x + 2\right ) e^{- 3 x} \]