Asked by Dan
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.
dy/dx=1 + cos x, y(pi)= 0
i don't understand how to do this problem. i don't know where to begin.
Answers
Answered by
drwls
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
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