Internal problem ID [11]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y=-\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x) = -sin(x)-y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\cos \left (x \right )}{2}-\frac {\sin \left (x \right )}{2}+{\mathrm e}^{-x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 25
DSolve[y'[x]== -Sin[x]-y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (-\sin (x)+\cos (x)+2 c_1 e^{-x}\right ) \]