Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y(pi/3)= 1.

Question

Find the particular solution to y ' = 2sin(x) given the general solution is y = C - 2cos(x) and the initial condition y(pi/3)= 1.

A. -2cos(x)

B. 3 - 2cos(x)

C. 2 - 2cos(x)

D. -1 - 2cos(x)

Answer 1

Your answer is C.

with y = -2cos(x) + c and y(pi/3) = -2cos(pi/3) + c = 1 or -2(1/2) + c = 1 so C = 2

Then y(x) = 2 - 2cos(x)