Answer to Question #198298 in Differential Equations for muhammad Ahmad

Question

Three students were given a differential equation y''+π ^2y=0 to solve. 

Answer 1

$y''+\pi^2y=0$

$\dfrac{d^2y}{dx^2}=y''=D^2y$

$D^2y+\pi^2y=0$

$(D^2+\pi^2)y=0$

Auxiliary equation,

$D^2+\pi^2=0$

$D^2=-\pi^2$

$D=\pm i\pi$

Complimentary function is given by,

$y=C_1e^{i\pi}+C_2e^{-i\pi}$