Solving differential equations by inspection!

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:

and so we must have:

Oh thanks for the reply!

Then let's say for y'' = 3 and I did. y'=3x+c
y= (3/2)x^2 +C

Then is y= (3/2)x^2 + C answer for y"=3?

Thank you.

No, for the second example, you should observe that:

hence: