1. Tardigrade
  2. Question
  3. Mathematics
  4. If y = aemx + be-mx, then (d2y/dx2) - m2 y is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $ y = ae^{mx} + be^{-mx}$, then $\frac{d^2y}{dx^2} - m^2 y$ is equal to

Limits and Derivatives

Solution:

$y = ae^{mx} + be^{-mx}$
$\therefore \frac{dy}{dx} = ame^{mx} - mbe^{-mx}$
Again $\frac{d^2y}{dx^2} = am^2 \,e^{mx} + m^2 be^{-mx}$
$ = m^2 ( ae^{mx} + be^{-mx}) = m^2y$
or $\frac{d^2y}{dx^2} - m^2y = 0$