87.16.5 problem 5

Internal problem ID [23574]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:43:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (3 x \right )-\sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)+9*y(x) = cos(3*x)-sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (3 x +18 c_1 +1\right ) \cos \left (3 x \right )}{18}+\frac {\sin \left (3 x \right ) \left (x +6 c_2 \right )}{6} \]

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to \frac {1}{18} ((3 x+1+18 c_1) \cos (3 x)+3 (x+6 c_2) \sin (3 x)) \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = \left (C_{1} + \frac {x}{6}\right ) \sin {\left (3 x \right )} + \left (C_{2} + \frac {x}{6}\right ) \cos {\left (3 x \right )} \]