Internal problem ID [5555]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-2 \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+y(x)=2*cos(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+x \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 20
DSolve[y''[x]+y[x]==2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (1+c_1) \cos (x)+(x+c_2) \sin (x) \\ \end{align*}