89.19.24 problem 24

Internal problem ID [24752]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Exercises at page 151
Problem number : 24
Date solved : Thursday, October 02, 2025 at 10:47:41 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=18 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+4*y(x) = 18*exp(-2*x)*cos(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (c_2 +c_1 x -2 \cos \left (3 x \right )\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+4*D[y[x],{x,1}]+4*y[x]== 18*Exp[-2*x]*Cos[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} (-2 \cos (3 x)+c_2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.212 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 18*exp(-2*x)*cos(3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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