89.21.9 problem 11

Internal problem ID [24781]
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 154
Problem number : 11
Date solved : Thursday, October 02, 2025 at 10:47:57 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+16*y(x) = 14*cos(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (4 x \right ) c_2 +\cos \left (4 x \right ) c_1 +2 \cos \left (3 x \right ) \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+16*y[x]== 14*Cos[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 \cos (3 x)+c_1 \cos (4 x)+c_2 \sin (4 x) \end{align*}

✓ Sympy. Time used: 0.046 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 14*cos(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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