85.55.1 problem 1

Internal problem ID [22824]
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 197
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:15:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x)+omega^2*y(x) = A*cos(lambda*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (\omega x \right ) c_2 +\cos \left (\omega x \right ) c_1 +\frac {A \cos \left (\lambda x \right )}{-\lambda ^{2}+\omega ^{2}} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 38

ode=D[y[x],{x,2}]+ \[Omega]^2*y[x]==A*Cos[\[Lambda]*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {A \cos (\lambda x)}{\lambda ^2-\omega ^2}+c_1 \cos (x \omega )+c_2 \sin (x \omega ) \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = \frac {A \cos {\left (\lambda _{} x \right )}}{- \lambda _{}^{2} + w^{2}} + C_{1} e^{- i w x} + C_{2} e^{i w x} \]