Question

$y=2\cos x+3\sin x$ satisfies which of the following differential equations?
1. $\frac{d^{2}y}{d{x}^2}+y=0$
2. ${\left(\frac{dy}{dx}\right)}^2+\frac{dy}{dx}=0$
Select the correct answer using the code given below.

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is A 1 only

$y=2\cos x+3\sin x$

$⟹\frac{dy}{dx}=-2\sin x+3\cos x$

$⟹\frac{d^{2}y}{d{x}^2}=-2\cos x-3\sin x$

We can see that,

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

Thus, statement 1 is true.

Also, ${\left(\frac{dy}{dx}\right)}^2+\frac{dy}{dx}\ne 0$

Thus, statement 2 is not true.

Hence, option A is correct.