If y = sin (ax + b), where a & b are constants, which of these is true (a) d²y/dx² + a²y = 0
(b)d²y/dx² + 2a²y = 0
(c) d²y/dx² - 2a² y = 0
(d) d²y/dx²+ y = 0
(e) d²y/dx² -a²y = 0
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Step-by-step explanation:

We have y = sin(ax + b).

=> dy/dx = a * cos(ax + b)

=> d²y/dx² = a[a * -sin(ax + b)] = a² - a * sin(ax + b).

Therefore d²y/dx² = a² - ay,

d²y/dx² - a² + y = 0.