Chapter 6.1, Problem 1QR

To determine

To check: whether the given function satisfies the given differential equation.

Answer to Problem 1QR

The given function satisfies the given differential equation.

Explanation of Solution

Given:

The differential equation is $\frac{dy}{dx}=y$ and the function is $y=e^x$ .

Calculation:

Consider the given function,

  $y=e^x$

By differentiating with respect to $x$ , it follows that

  $\begin{array}{l}\frac{dy}{dx}=\frac{d}{dx}\left(e^x\right)\\ \frac{dy}{dx}=e^x\\ \frac{dy}{dx}=y\left[\because y=e^x\right]\end{array}$

Therefore, the given function satisfies the given differential equation.