Browse Questions

# The complementary function of $(D^{2}+1)y=e^{2x}$ is

$\begin{array}{1 1}(1)(Ax+B)e^{x}&(2)A\cos x+B\sin x\\(3)(Ax+B)e^{2x}&(4)(Ax+B)e^{-x}\end{array}$

$(d^2+1) y=e^{2x}$
Auxiliary equation is
$m^2+1=0$
$m^2=-1=.< m =\pm i$
$C.F= e^{0x} ( A \cos x + B \sin x)$
$\qquad= A \cos x +B \sin x$
Hence 2 is the correct answer.