58.10.10 problem 10

Internal problem ID [14697]
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 : 10
Date solved : Thursday, October 02, 2025 at 09:50:17 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=0 \end{align*}

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

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-3 x} \left (c_1 \sin \left (4 x \right )+c_2 \cos \left (4 x \right )\right ) \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+6*D[y[x],x]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} (c_2 \cos (4 x)+c_1 \sin (4 x)) \end{align*}

✓ Sympy. Time used: 0.094 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (4 x \right )} + C_{2} \cos {\left (4 x \right )}\right ) e^{- 3 x} \]