Question

Solve the initial value problem.
ds/dt= cost-sint, s(pi/2)=3
OR
See attachment.

Answer 1

Just integrate both sides
\[s(t)=\int (\cos(t)-\sin(t))dt\]

Answer 2

And then use the given point to find the value of the constant c.

Answer 3

Does that make sense?

Answer 4

So, umm you get sin(t)-cos(t) + C

Answer 5

Be careful with the signs!

Answer 6

Oh right, sin(t)+cos(t) + C, and then you plug in (pi/2)?

Answer 7

Yep!

Answer 8

So, 1 + C?

Answer 9

1+C equal to what?

Answer 10

Lol, 4 :P?

Answer 11

Is that right?

Answer 12

You've got \(s(t)=\sin(t)+\cos(t)+c\), and you have \(s(\pi/2)=3\). So?

Answer 13

Ohhhhhhh! Nvm, 1+C=3. So, C=2

Answer 14

Good!

Answer 15

Hoorah! :DThanks