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Chapter 4: Q. 07 (page 364)

Preview of Differential Equations:
Given each of the following equations involving a functionf, find a possible formula for f(x).
$f' (x) = f (x)$

Short Answer

Expert verified

The possible formula for the function $f' (x) = f (x)$ is $f (x) = e^{x}$ .

Step by step solution

01

Step 1. Given Information.

The function:

$f' (x) = f (x)$

02

Step 2. Consider the function.

Consider the function,

$f (x) = e^{x} f' (x) = \frac{d}{d x} e^{x} = e^{x} = f (x)$

So the function is $f (x) = e^{x}$ .

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Most popular questions from this chapter

Find the sum or quantity without completely expanding or calculating any sums.

Given $\sum_{k = 3}^{10} a_{k} = 12$ and $\sum_{k = 2}^{10} a_{k} = 23$ , find $a_{2}$ .

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See all solutions

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