Question

Form a differential equation $y=A\cos x+B\sin x$, and find the order of the differential equation obtained thus.

Answer 1

Given,

$y=A\cos x+B\sin x$......(1).

Now differentiating both sides with respect to $x$ we get,

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

Again differentiating both sides with respect to $x$ we get,

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

or, $\frac{d^{2}y}{d{x}^2}=-y$ [ Using (1)]

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

From the equation we get, the order of the differential equation is $2$.