89.18.10 problem 10

Internal problem ID [24710]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Oral Exercises at page 146
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:47:20 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=\cos \left (4 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{x} c_1 -\frac {\cos \left (4 x \right )}{17} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to -\frac {1}{17} \cos (4 x)+c_1 e^x+c_2 e^{-x} \end{align*}

✓ Sympy. Time used: 0.049 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} - \frac {\cos {\left (4 x \right )}}{17} \]