Internal problem ID [5648]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Problems for Discussion and Exploration.
Page 105
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 19
dsolve(diff(y(x),x)+y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\cos \relax (x )}{2}+\frac {\sin \relax (x )}{2}+{\mathrm e}^{-x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 23
DSolve[y'[x]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right ) \\ \end{align*}