80.8.8 problem 8

Internal problem ID [18587]
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 : Tuesday, January 28, 2025 at 12:03:15 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*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+3*y(x)=sin(x)+1/3*sin(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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