Question

Show that y= x + sinx-pi satisfies the initial value problem

dy/dx=1 + cos x, y(pi)= 0


i don't understand how to do this problem. i don't know where to begin.

Answer 1

You should indicate whether you mean
sin (x-pi) or sinx - pi
It makes a big difference in the answer.

Let's assume you meant
y = x + sinx - pi

In that case
dy/dx = 1 + cos x
and y(x=pi) = pi + 0 - pi = 0

That agrees with what you are trying to prove: the dy/dx equation, and the initial condition at y = pi