Chapter 6: Q. 29 (page 570)

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

Short Answer

Expert verified

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

Step by step solution

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 $y = 4 e^{3 x}$

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

Short Answer

Step by step solution

Step 1. Given information

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

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Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.29. dydx=3y,y0=4

Short Answer

Step by step solution

Step 1. Given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

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