8.2.1 problem 1

Internal problem ID [661]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:56:49 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 19

dsolve(diff(y(x),x) = -sin(x)-y(x),y(x), singsol=all)
 

\[ y = \frac {\cos \left (x \right )}{2}-\frac {\sin \left (x \right )}{2}+{\mathrm e}^{-x} c_1 \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 25

DSolve[D[y[x],x]== -Sin[x]-y[x],y[x],x,IncludeSingularSolutions -> True]
 

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