Internal problem ID [5554]
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]]
\[ \boxed {y^{\prime \prime }+y-2 \cos \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+y(x)=2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\sin \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.007 (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*}