Question

The differential equation obtained by eliminating $A$ and $B$ from $y=A\cos wt+B\sin wt$ is

• A. $y"+y^{\prime }=0$
• B. $y"+w^{2}y=0$
• C. $y"=w^{2}y$
• D. $y"+y=0$

Answer 1

The correct option is B $y"+w^{2}y=0$

$y=A\cos wt+B\sin wt$

$y^{\prime }=w(-A\sin wt+B\cos wt)$

$y"=w^2(-A\cos wt-B\sin wt)$

$y"=-w^2(A\cos wt+B\sin wt)$

$y"=-w^{2}y$

$\therefore y"+w^{2}y=0$