I have this question 1. Solve the following DE’s, by inspection.
y’= -sin x
I Know that y=cos x and y'= -sin x. Then is y=cos x the answer? What does it mean when solve by inspection???
Solving by inspection involves exactly what you did (well, almost, you forgot the constant of integration)...you know that:
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}(\cos(x)+C)=-\sin(x)$ and so we must have:
$\displaystyle y=\cos(x)+C$