# The differential equation formed by eliminating $A$ and $B$ from the relation $y=e^{x}(A\cos x+ B\sin x)$ is

$\begin{array}{1 1}(1)y_{2}+y_{1}=0&(2)y_{2}-y_{1}=0\\(3)y_{2}-2y_{1}+2y=0&(4)y_{2}-2y_{1}-2y=0\end{array}$

$y=e^{x}(A \cos x +B \sin x)$
Here $m=1,n=1$
The required differential equation is
$(D^2-2D \times 1 +1^2 +1^2)y=0$
$(D^2-2D+2) y=0$
Hence 3 is the correct answer.