Question

1. Find a homogeneous linear differential equation with constant coefficients whose general solution is given.


y = c1 cos 2x + c2 sin 2x


A. y'' + 2y = 0

B. y'' − 2y = 0

C. y'' + 4y = 0

D. y'' − 4y = 0

E. y'' − 4y' + 4y = 0

Answer 1

$y'=-2c_1sin2x+2c_2cos2x$

$y''=-4c_1cos2x-4c_2sin2x$

Then:

$y'' + 4y =-4c_1cos2x-4c_2sin2x+ 4c_1 cos 2x +4 c_2 sin 2x=0$

Answer: C. $y'' + 4y = 0$