Chapter 6: Q. 30 (page 570)

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

Short Answer

Expert verified

The answer is $y (x) = \frac{3}{2} x^{2} + 4$

Step by step solution

Step 1. Given information

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

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

The differential equation can be solved by antidifferentiating.

$\int d y = \int 3 x d x y = \frac{3}{2} x^{2} + C$

Now put $y (0) = 4$ ,

$4 = \frac{3}{2} {(0)}^{2} + C 4 = C$

So, the answer is $y (x) = \frac{3}{2} x^{2} + 4$

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

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 29–52.30.dydx=3x,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

Discrete Mathematics

Theoretical and Mathematical Physics

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