Question

Form the differential equation representing the family of curves $y=A\cos (x+B)$, where A and B are parameters.

Answer 1

$y=A\cos (x+B)$

Differentiating w.r.t. x, we get,

$\frac{dy}{dx}=-A\sin (x+B)$

Again, differentiating w.r.t. x. we get,

$\frac{d^{2}y}{d{x}^2}=-A\cos (x+B)$

$\frac{d^{2}y}{d{x}^2}=-y$

$\frac{d^{2}y}{d{x}^2}+y=0$

which is the required differential equation.