49.11.2 problem 1(b)

Internal problem ID [7666]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 93
Problem number : 1(b)
Date solved : Monday, January 27, 2025 at 03:09:17 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+4*y(x)=sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]+4*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (-\frac {x}{4}+c_1\right ) \cos (2 x)+\frac {1}{8} (1+16 c_2) \sin (x) \cos (x) \]