Chapter 6: Q. 35 (page 570)

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.
35. $\frac{d y}{d x} = \frac{3}{y}, y (0) = 2$

Short Answer

Expert verified

The answer is $y (x) = \sqrt{6 x + 4}$

Step by step solution

Step 1. Given information

We have been given $\frac{d y}{d x} = \frac{3}{y}, y (0) = 2$

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

The differential equation can be solved by antidifferentiating.

$\int y d y = \int 3 d x \frac{1}{2} y^{2} = 3 x + C_{1} y^{2} = 6 x + 2 C_{1} y^{2} = 6 x + C$

Now put $y (0) = 2$ ,

role="math" localid="1649147751077" ${(2)}^{2} = 6 (0) + C 4 = C$

So,

role="math" localid="1649147767750" $y^{2} = 6 x + 4 y = \sqrt{6 x + 4}$

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Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.
35. $\frac{d y}{d x} = \frac{3}{y}, y (0) = 2$

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 29–52.35.dydx=3y,y0=2

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

Geometry

Mechanics Maths

Applied Mathematics

Probability and Statistics

Logic and Functions

Decision Maths

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.
35. $\frac{d y}{d x} = \frac{3}{y}, y (0) = 2$