49.6.2 problem 1(b)

Internal problem ID [7630]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 69
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:08:11 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+9*y(x)=sin(3*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 33

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

\[ y(x)\to \left (-\frac {x}{6}+c_1\right ) \cos (3 x)+\frac {1}{36} (1+36 c_2) \sin (3 x) \]