Question

yy'=sin(x) How do I differentiate this equation using separation of variables?

Answer 1

\[y \frac{ dy }{ dx } = \sin x\] \[\large y dy = \sin x dx \] \[\large \int\limits y dy = \int\limits \sin x dx\]

Answer 2

Do you know how to integrate from there?

Answer 3

Not quite...

Answer 4

\[\large \int\limits\limits y dy = \int\limits\limits \sin x dx \] integrate the right w.r.t. y and the left w.r.t. x. For y, it's just a simple increase the power by one, divide by the new power. For sinx, the integral is -cosx:
\[\large \frac{ y^2 }{2 } = -\cos x + C\]

Now just rearrange for y = ...