First slide

Introduction to Differential equations

Question

$y = a e^{m x} + b e^{- m x}$ satisfies which of the following differential equations?

Moderate

A

$\frac{d y}{d x} - m y = 0$
B

$\frac{d y}{d x} + m y = 0$
C

$\frac{d^{2} y}{d x^{2}} + 1 n^{2} y = 0$
D

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

Solution

We have, $y = a e^{m x} + b e^{- m x}$
$\begin{array}{l} \Rightarrow \frac{d y}{d x} = m a e^{m x} - m b e^{- m x} \\ \Rightarrow \frac{d^{2} y}{d x^{2}} = m^{2} (a e^{m x} + b e^{- m x}) \\ \Rightarrow \frac{d^{2} y}{d x^{2}} = m^{2} y \Rightarrow \frac{d^{2} y}{d x^{2}} - m^{2} y = 0 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App