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Q. 29

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Calculus

Found in: Page 570

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.
29. $\frac{d y}{d x} = 3 y, y (0) = 4$

The answer is $y (x) = 4 e^{3 x}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

We have been given $\frac{d y}{d x} = 3 y, y (0) = 4$

Step 2. Solve using antidifferentiation and/or variable separable method.

The differential equation can be solved by antidifferentiating.

$\int \frac{1}{y} d y = \int 3 d x \ln |y| = 3 x + C y = e^{3 x + C} y = A e^{3 x} (e^{c} = A)$

Now put $y (0) = 4$ ,

$4 = A e^{3 (0)} 4 = A$

So, the answer is $y = 4 e^{3 x}$

Most popular questions for Math Textbooks

Explain how equality ${\frac{d y}{d x}|}_{(x_{k}, y_{k})} = \frac{Δ y_{k}}{Δ x}$ is relevant to Euler’s method.

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30. $\frac{d y}{d x} = 3 x, y (0) = 4$

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A

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