Find the solution

Question

Find the particular solution to y ′ = 2sin(x) given the general solution is y = C − 2cos(x) and the initial condition .

Question options:

1)	-2cos(x)
2)	3 - 2cos(x)
3)	2 - 2cos(x)
4)	-1 - 2cos(x)

Answer 1

For this problem, you actually don't need to do any calculus. You are told what the solution is:

y(x) = C-2cos(x). The particular solution is found by making the initial condition work. That is, we need

y(pi/3) = 1.

So,

1 = y(pi/3) = C-2cos(pi/3),

C = 1+2cos(pi/3) = 1+2(1/2) = 1+1 = 2.

So, y(x) = 2(1-cos(x)).