Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions y of pi over 2 equals 0 and y prime of pi over 2 equals negative 2

Question

Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions  and  

A	-2sin(x) + 2
B	-2sin(x) - 2x + π + 2
C	-2sin(x) - 2x + 2π
D	-2sin(x) - 2x + π

Answer 1

We are given

y = -2sin(x) + Ax + B

From that we calculate

y' = -2cos(x) + A

Then we plug the given constraints at π/2 into the equations for y and y':

0 = -2sin(π/2) + Aπ/2 + B

-2 = -2cos(π/2) + A

Solve the above two equations for A and B:

A = -2

B = π+2

Thus the correct answer is

B: y = -2sin(x) - 2x + π + 2