49.11.1 problem 1(a)

Internal problem ID [7665]
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(a)
Date solved : Monday, January 27, 2025 at 03:09:13 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 26

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

\[ y(x)\to \frac {\cos (x)}{3}+c_1 \cos (2 x)+c_2 \sin (2 x) \]