89.19.23 problem 23

Internal problem ID [24751]
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 : 23
Date solved : Thursday, October 02, 2025 at 10:47:40 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=48 \,{\mathrm e}^{-x} \cos \left (4 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 48*exp(-x)*cos(4*x); 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=D[y[x],{x,2}]+2*D[y[x],{x,1}]+y[x]== 48*Exp[-x]*Cos[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.198 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 48*exp(-x)*cos(4*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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