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If cosx and sinx are solutions of the di...

If `cosx` and `sinx` are solutions of the differential equation `a_(0)(d^(2)y)/(dx^(2))+a_(1)(dy)/(dx)+a_(2)y=0`
where, `a_(0),a_(1),a_(2)` are real constants then which of the followings is/are always true?

A

`A cosx+B sinx` is a solution, where A and B are real constants.

B

`A cos(x+(pi)/(4))` is a solution, where A is real constant.

C

`A cos x sin x` is a solution, where A is real constant.

D

`A cos(x+(pi)/(4))+Bsin(x-(pi)/(4))` is a solution, where A and B are real constant.

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