(i) Explanation Given: i) The function: 3 x 2 + 2 y 2 = C . ii) The differential equation: 3 x + 2 y y ' ' = 0 . Explanation: The function 3 x 2 + 2 y 2 = C has been provided. On differentiating both sides with respect to x , we derive: d d x ( 3 x 2 + 2 y 2 ) = d d x ( C ) = 0 . 6 x + 4 y d y d x = 0 (ii) To determine To calculate: The particular solution with initial condition y = 3 when x = 3 .

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 6.1, Problem 38E

(i)

To determine

Whether the general solution 3x2+2y2=C satisfies the differential equation 3x+2yy''=0

(ii)

To determine

To calculate: The particular solution with initial condition y=3 when x=3.

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Chapter 6.1, Problem 37E

Chapter 6.1, Problem 39E

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Whether the general solution 3 x 2 + 2 y 2 = C satisfies the differential equation 3 x + 2 y y ' ' = 0

Solution Summary: The author explains how the general solution satisfies the differential equation 3x+2yy'