Calculus question

Question

Verify whether the function y=Acos2x+Bsin2x satisfies the equation y^2+4y=0

Answer 1

y^2 +4y = 0

complete the square

y+2 = +/-2

y = 0 or -4

Acos2x +Bsin2x = y = 0 or -4

Acos2x + Bsin2x = 0

sin2x/cos2x = -A/B

tan2x = -A/B

if A=-B, then

tan2x = 1

2x = 45 or pi/4

x = 22.5 + 180n degrees where n= any integer

or

x = pi/4 +npi where n = any integer

depending on values of A and B, x could = any angle,

with an infinite number of solutions

also if

tan2x =-4

then 2x is in quadrant 2 or 4

but maybe the question is asking does it "satisfy" y^2+4y=0

in the sense of is it an identity. IF so, then it doesn't

"satisfy"