Q. 375.0( 2 Votes )

If y = e-x (A cos x + B sin x), then y is a solution of
A.

B.

C.

D.

Answer :

If y = f(x) is solution of a differential equation then differentiating y = f(x) will give the same differential equation


Let us find the differential equation by differentiating y with respect to x twice


Why twice because all the options have order as 2 and also because there are two constants A and B


y = e-x (A cos x + B sin x)


Differentiating using product rule



But e-x (A cos x + B sin x) = y



Differentiating again with respect to x




But e-x (A cos x + B sin x) = y



Also which means





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