14.7.9 problem Problem 33

Internal problem ID [3724]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 33
Date solved : Tuesday, September 30, 2025 at 06:56:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=5 \cos \left (2 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+9*y(x) = 5*cos(2*x); 
ic:=[y(0) = 2, D(y)(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

ode=D[y[x],{x,2}]+9*y[x]==5*Cos[2*x]; 
ic={y[0]==2,Derivative[1][y][0] ==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.048 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - 5*cos(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

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