64.10.37 problem 37

Internal problem ID [13364]
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 : 37
Date solved : Wednesday, March 05, 2025 at 09:49:09 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 9 y^{\prime \prime }+6 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 21

ode:=9*diff(diff(y(x),x),x)+6*diff(y(x),x)+5*y(x) = 0; 
ic:=y(0) = 6, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 29

ode=9*D[y[x],{x,2}]+6*D[y[x],x]+5*y[x]==0; 
ic={y[0]==6,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.188 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + 6*Derivative(y(x), x) + 9*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 6, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (3 \sin {\left (\frac {2 x}{3} \right )} + 6 \cos {\left (\frac {2 x}{3} \right )}\right ) e^{- \frac {x}{3}} \]