50.10.7 problem 1(g)

Internal problem ID [7976]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 1(g)
Date solved : Monday, January 27, 2025 at 03:34:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 20

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

\[ y(x)\to (1+c_1) \cos (x)+(x+c_2) \sin (x) \]