8.2.3 problem 3

Internal problem ID [663]
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
Date solved : Monday, January 27, 2025 at 02:56:52 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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: 0.032 (sec). Leaf size: 21

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

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