Question

The differential equation of the family of curves $y = a\cos\mu x + b\sin\mu x$, where $a$ and $b$ are arbitrary constants, is

• A. $\dfrac{d^{2}y}{dx^{2}} + \mu y = 0$
• B. $\dfrac{d^{2}y}{dx^{2}} - \mu^{2}y = 0$
• C. $\dfrac{d^{2}y}{dx^{2}} + \mu^{2}y = 0$
• D. None of these

Hint:

The family $y = a\cos\mu x + b\sin\mu x$ satisfies the simple harmonic equation $y'' + \mu^2 y = 0$. This is a standard result.

Answer 1

The Correct Option is C