89.21.13 problem 15

Internal problem ID [24785]
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 : 15
Date solved : Thursday, October 02, 2025 at 10:48:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=12 \cos \left (2 x \right )-\sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+y(x) = 12*cos(2*x)-sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 -4 \cos \left (2 x \right )+\frac {\sin \left (3 x \right )}{8} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 36

ode=D[y[x],{x,2}]+y[x]== 12*Cos[2*x]-Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.055 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) + sin(3*x) - 12*cos(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )} + \frac {\sin {\left (3 x \right )}}{8} - 4 \cos {\left (2 x \right )} \]