89.21.10 problem 12

Internal problem ID [24782]
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 : 12
Date solved : Thursday, October 02, 2025 at 10:47:58 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime }+y&=33 \sin \left (3 x \right ) \end{align*}

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

ode:=4*diff(diff(y(x),x),x)+y(x) = 33*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (\frac {x}{2}\right ) c_2 +\cos \left (\frac {x}{2}\right ) c_1 -\frac {33 \sin \left (3 x \right )}{35} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 32

ode=4*D[y[x],{x,2}]+y[x]== 33*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {33}{35} \sin (3 x)+c_1 \cos \left (\frac {x}{2}\right )+c_2 \sin \left (\frac {x}{2}\right ) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 33*sin(3*x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (\frac {x}{2} \right )} + C_{2} \cos {\left (\frac {x}{2} \right )} - \frac {33 \sin {\left (3 x \right )}}{35} \]