Internal problem ID [13]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.3. Slope fields and solution curves. Page 26
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+\sin \relax (x )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(diff(y(x),x) = -sin(x)+y(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: 0.043 (sec). Leaf size: 21
DSolve[y'[x] == -Sin[x]+y[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*}