(a) To determine To prove: The differential equation d y d x = 3 y 2 − x 2 2 x y . Explanation Definition used: If the right side of the equation d y d x = f ( x , y ) can be expressed as a function of the ratio y x only, then the equation is said to be homogeneous. Such equations can always be transformed into separable equations by a change of the dependent variable. Calculation: The given differential equation is d y d x = 3 y 2 − x 2 2 x y . Compare the above differential equation with d y d x = f ( x , y ) and obtain that f ( x , y ) = 3 y 2 − x 2 2 x y . Note that the function f can be rewritten as follows (b) To determine To solve: The differential equation d y d x = 3 y 2 − x 2 2 x y . (c) To determine To sketch: The directional field of the differential equation d y d x = 3 y 2 − x 2 2 x y and its some solution curves.

10th Edition

ISBN: 9780470458327

Author: William E. Boyce, Richard C. DiPrima

Publisher: Wiley, John & Sons, Incorporated

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Chapter 2.2, Problem 38P

(a)

To determine

To prove: The differential equation dydx=3y2−x22xy.

(b)

To determine

To solve: The differential equation dydx=3y2−x22xy.

(c)

To determine

To sketch: The directional field of the differential equation dydx=3y2−x22xy and its some solution curves.

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Chapter 2.2, Problem 37P

Chapter 2.3, Problem 1P

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Chapter 2 Solutions

Elementary Differential Equations

Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - In each of Problems 1 through 12: Draw a direction...Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

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