80.8.8 problem 8

Internal problem ID [18516]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 8
Date solved : Monday, March 31, 2025 at 05:41:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)+3*y(x) = sin(x)+1/3*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (\sqrt {3}\, x \right ) c_2 +\cos \left (\sqrt {3}\, x \right ) c_1 +\frac {\sin \left (x \right )}{2}-\frac {\sin \left (3 x \right )}{18} \]

✓ Mathematica. Time used: 0.559 (sec). Leaf size: 42

ode=D[y[x],{x,2}]+3*y[x]==Sin[x]+1/3*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sin (x)}{2}-\frac {1}{18} \sin (3 x)+c_1 \cos \left (\sqrt {3} x\right )+c_2 \sin \left (\sqrt {3} x\right ) \]

✓ Sympy. Time used: 0.101 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = C_{1} \sin {\left (\sqrt {3} x \right )} + C_{2} \cos {\left (\sqrt {3} x \right )} + \frac {\sin {\left (x \right )}}{2} - \frac {\sin {\left (3 x \right )}}{18} \]