54.1.1 problem 1

Internal problem ID [8529]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 8. Nonhomogeneous Equations: Undetermined Coefficients. Exercises Page 142
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:09:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 27

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

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