85.58.1 problem 1

Internal problem ID [22839]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 200
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:15:37 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 41

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

\[ y = \sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_1 +\frac {1}{24}+\frac {\sin \left (2 x \right ) x}{16}+\frac {\left (4+3 \cos \left (2 x \right )\right ) \sin \left (2 x \right )^{2}}{96} \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 50

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

\begin{align*} y(x)&\to \frac {1}{384} (24 x \sin (2 x)-8 \cos (4 x)-3 \cos (6 x)+6 (3+64 c_1) \cos (2 x)+384 c_2 \sin (2 x)+24) \end{align*}

✓ Sympy. Time used: 2.634 (sec). Leaf size: 121

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

\[ y{\left (x \right )} = C_{2} \cos {\left (2 x \right )} - \frac {5 x \sin {\left (4 x \right )}}{8} + \frac {x \sin {\left (8 x \right )}}{16} + \frac {23 \left (1 - \cos {\left (2 x \right )}\right )^{4}}{24} - \frac {365 \left (1 - \cos {\left (2 x \right )}\right )^{3}}{96} + \frac {211 \left (1 - \cos {\left (2 x \right )}\right )^{2}}{48} + \left (C_{1} + \frac {x \left (1 - \cos {\left (2 x \right )}\right )^{3}}{2} - \frac {3 x \left (1 - \cos {\left (2 x \right )}\right )^{2}}{2} + \frac {17 x}{16}\right ) \sin {\left (2 x \right )} + \frac {25 \cos {\left (4 x \right )}}{192} - \frac {23 \cos {\left (8 x \right )}}{192} - \frac {39}{32} \]