Q. $y = ae^{mx} + be^{- mx}$ satisfies which of the following differential equations
A) $\frac{dy}{dx} - my = 0$
B) $\frac{dy}{dx} + my = 0$
C) $\frac{d^{2}y}{dx^{2}} - m^{2}y = 0$
D) None of these
Explanation
(c)
Given, $y = ae^{mx} + be^{- mx}$
$\Rightarrow$ $\frac{dy}{dx} = mae^{mx} - m\ be^{- mx}$
$\Rightarrow$ $\frac{d^{2}y}{dx^{2}} = m^{2}ae^{mx} + m^{2}be^{- mx} = m^{2}y$
$\Rightarrow$ $\frac{d^{2}y}{dx^{2}} - m^{2}y = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.