Program Explanation Given information: The differential equation is 6 x y 3 + 2 y 4 + ( 9 x 2 y 2 + 8 x y 3 ) y ′ = 0 . Explanation: The given differential equation can be written as, 6 x y 3 + 2 y 4 + ( 9 x 2 y 2 + 8 x y 3 ) d y d x = 0 ( 6 x y 3 + 2 y 4 ) d x + ( 9 x 2 y 2 + 8 x y 3 ) d y = 0 The general form of exact differential equation is, M ( x , y ) d x + N ( x , y ) d y = 0 The above differential equation is exact if and only if the below condition satisfies, ∂ M d y = ∂ N ∂ x ....... (1) Compare the given differential equation with the general differential equation to obtain the value of M ( x , y ) and N ( x , y ) as, M ( x , y ) = 6 x y 3 + 2 y 4 N ( x , y ) = 9 x 2 y 2 + 8 x y 3 Substitute 6 x y 3 + 2 y 4 for M and 9 x 2 y 2 + 8 x y 3 for N in equation (1) as, ∂ ∂ y ( 6 x y 3 + 2 y 4 ) = ? ∂ ∂ x ( 9 x 2 y 2 + 8 x y 3 ) 6 x ⋅ 3 y 2 + 8 y 3 = ? 9 y 2 ⋅ 2 x + 8 y 3 18 x y 2 + 8 y 3 = 18 x y 2 + 8 y 3 Thus, the given differential equation is exact

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Concept explainers

Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.

Question

Chapter 1, Problem 12RP

Program Plan Intro

Program Description: Purpose of problem is to calculate the general solution of the differential equation 6xy3+2y4+(9x2y2+8xy3)y′=0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1, Problem 11RP

Chapter 1, Problem 13RP

Students have asked these similar questions

Pls help ASAP

9. a) Determie values of a and b so that the function is continuous. ax - 2b f(x) 2 x≤-2 -2x+a, x ≥2 \-ax² - bx + 1, −2 < x < 2) 9b) Consider f(x): = 2x²+x-3 x-b and determine all the values of b such that f(x) does not have a vertical asymptote. Show work.

Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

Ch. 1.1 - Prob. 1P Ch. 1.1 - Prob. 2P Ch. 1.1 - Prob. 3P Ch. 1.1 - Prob. 4P Ch. 1.1 - Prob. 5P Ch. 1.1 - Prob. 6P Ch. 1.1 - Prob. 7P Ch. 1.1 - Prob. 8P Ch. 1.1 - Prob. 9P Ch. 1.1 - Prob. 10P

Ch. 1.1 - Prob. 11P Ch. 1.1 - Prob. 12P Ch. 1.1 - Prob. 13P Ch. 1.1 - Prob. 14P Ch. 1.1 - Prob. 15P Ch. 1.1 - Prob. 16P Ch. 1.1 - Prob. 17P Ch. 1.1 - Prob. 18P Ch. 1.1 - Prob. 19P Ch. 1.1 - Prob. 20P Ch. 1.1 - Prob. 21P Ch. 1.1 - Prob. 22P Ch. 1.1 - Prob. 23P Ch. 1.1 - Prob. 24P Ch. 1.1 - Prob. 25P Ch. 1.1 - Prob. 26P Ch. 1.1 - Prob. 27P Ch. 1.1 - Prob. 28P Ch. 1.1 - Prob. 29P Ch. 1.1 - Prob. 30P Ch. 1.1 - Prob. 31P Ch. 1.1 - Prob. 32P Ch. 1.1 - Prob. 33P Ch. 1.1 - Prob. 34P Ch. 1.1 - Prob. 35P Ch. 1.1 - Prob. 36P Ch. 1.1 - Prob. 37P Ch. 1.1 - Prob. 38P Ch. 1.1 - Prob. 39P Ch. 1.1 - Prob. 40P Ch. 1.1 - Prob. 41P Ch. 1.1 - Prob. 42P Ch. 1.1 - Prob. 43P Ch. 1.1 - Prob. 44P Ch. 1.1 - Prob. 45P Ch. 1.1 - Prob. 46P Ch. 1.1 - Prob. 47P Ch. 1.1 - Prob. 48P Ch. 1.2 - Prob. 1P Ch. 1.2 - Prob. 2P Ch. 1.2 - Prob. 3P Ch. 1.2 - Prob. 4P Ch. 1.2 - In Problems 1 through 10, find a function y=f(x)...Ch. 1.2 - Prob. 6P Ch. 1.2 - Prob. 7P Ch. 1.2 - Prob. 8P Ch. 1.2 - Prob. 9P Ch. 1.2 - Prob. 10P Ch. 1.2 - Prob. 11P Ch. 1.2 - Prob. 12P Ch. 1.2 - Prob. 13P Ch. 1.2 - Prob. 14P Ch. 1.2 - Prob. 15P Ch. 1.2 - Prob. 16P Ch. 1.2 - Prob. 17P Ch. 1.2 - Prob. 18P Ch. 1.2 - Prob. 19P Ch. 1.2 - Prob. 20P Ch. 1.2 - Prob. 21P Ch. 1.2 - Prob. 22P Ch. 1.2 - Prob. 23P Ch. 1.2 - A ball is dropped from the top of a building 400...Ch. 1.2 - Prob. 25P Ch. 1.2 - Prob. 26P Ch. 1.2 - Prob. 27P Ch. 1.2 - Prob. 28P Ch. 1.2 - A diesel car gradually speeds up so that for the...Ch. 1.2 - Prob. 30P Ch. 1.2 - Prob. 31P Ch. 1.2 - Prob. 32P Ch. 1.2 - On the planet Gzyx, a ball dropped from a height...Ch. 1.2 - Prob. 34P Ch. 1.2 - Prob. 35P Ch. 1.2 - Prob. 36P Ch. 1.2 - Prob. 37P Ch. 1.2 - Prob. 38P Ch. 1.2 - If a=0.5mi and v0=9mi/h as in Example 4, what must...Ch. 1.2 - Prob. 40P Ch. 1.2 - Prob. 41P Ch. 1.2 - Prob. 42P Ch. 1.2 - Prob. 43P Ch. 1.2 - Prob. 44P Ch. 1.3 - Prob. 1P Ch. 1.3 - Prob. 2P Ch. 1.3 - Prob. 3P Ch. 1.3 - Prob. 4P Ch. 1.3 - Prob. 5P Ch. 1.3 - Prob. 6P Ch. 1.3 - Prob. 7P Ch. 1.3 - Prob. 8P Ch. 1.3 - Prob. 9P Ch. 1.3 - Prob. 10P Ch. 1.3 - Prob. 11P Ch. 1.3 - Prob. 12P Ch. 1.3 - Prob. 13P Ch. 1.3 - Prob. 14P Ch. 1.3 - Prob. 15P Ch. 1.3 - Prob. 16P Ch. 1.3 - Prob. 17P Ch. 1.3 - Prob. 18P Ch. 1.3 - Prob. 19P Ch. 1.3 - Prob. 20P Ch. 1.3 - Prob. 21P Ch. 1.3 - Prob. 22P Ch. 1.3 - Prob. 23P Ch. 1.3 - Prob. 24P Ch. 1.3 - Prob. 25P Ch. 1.3 - Prob. 26P Ch. 1.3 - Prob. 27P Ch. 1.3 - Prob. 28P Ch. 1.3 - Verify that if c is a constant, then the function...Ch. 1.3 - Prob. 30P Ch. 1.3 - Prob. 31P Ch. 1.3 - Prob. 32P Ch. 1.3 - Prob. 33P Ch. 1.3 - (a) Use the direction field of Problem 5 to...Ch. 1.3 - Prob. 35P Ch. 1.4 - Prob. 1P Ch. 1.4 - Prob. 2P Ch. 1.4 - Prob. 3P Ch. 1.4 - Prob. 4P Ch. 1.4 - Prob. 5P Ch. 1.4 - Prob. 6P Ch. 1.4 - Prob. 7P Ch. 1.4 - Prob. 8P Ch. 1.4 - Prob. 9P Ch. 1.4 - Prob. 10P Ch. 1.4 - Prob. 11P Ch. 1.4 - Prob. 12P Ch. 1.4 - Prob. 13P Ch. 1.4 - Prob. 14P Ch. 1.4 - Prob. 15P Ch. 1.4 - Prob. 16P Ch. 1.4 - Prob. 17P Ch. 1.4 - Prob. 18P Ch. 1.4 - Prob. 19P Ch. 1.4 - Prob. 20P Ch. 1.4 - Prob. 21P Ch. 1.4 - Prob. 22P Ch. 1.4 - Prob. 23P Ch. 1.4 - Prob. 24P Ch. 1.4 - Prob. 25P Ch. 1.4 - Prob. 26P Ch. 1.4 - Prob. 27P Ch. 1.4 - Prob. 28P Ch. 1.4 - Prob. 29P Ch. 1.4 - Prob. 30P Ch. 1.4 - Prob. 31P Ch. 1.4 - Prob. 32P Ch. 1.4 - (Population growth) A certain city had a...Ch. 1.4 - Prob. 34P Ch. 1.4 - Prob. 35P Ch. 1.4 - (Radiocarbon dating) Carbon taken from a purported...Ch. 1.4 - Prob. 37P Ch. 1.4 - (Continuously compounded interest) Suppose that...Ch. 1.4 - Prob. 39P Ch. 1.4 - Prob. 40P Ch. 1.4 - Prob. 41P Ch. 1.4 - Prob. 42P Ch. 1.4 - Prob. 43P Ch. 1.4 - Prob. 44P Ch. 1.4 - Prob. 45P Ch. 1.4 - Prob. 46P Ch. 1.4 - Prob. 47P Ch. 1.4 - Prob. 48P Ch. 1.4 - Prob. 49P Ch. 1.4 - The amount A (t ) of atmospheric pollutants in a...Ch. 1.4 - An accident at a nuclear power plant has left the...Ch. 1.4 - Prob. 52P Ch. 1.4 - Prob. 53P Ch. 1.4 - Prob. 54P Ch. 1.4 - Prob. 55P Ch. 1.4 - Prob. 56P Ch. 1.4 - Prob. 57P Ch. 1.4 - Prob. 58P Ch. 1.4 - Prob. 59P Ch. 1.4 - Prob. 60P Ch. 1.4 - A spherical tank of radius 4 ft is full of water...Ch. 1.4 - Prob. 62P Ch. 1.4 - Prob. 63P Ch. 1.4 - (The clepsydra, or water clock) A 12 h water clock...Ch. 1.4 - Prob. 65P Ch. 1.4 - Prob. 66P Ch. 1.4 - Prob. 67P Ch. 1.4 - Figure 1.4.11 shows a bead sliding down a...Ch. 1.4 - Prob. 69P Ch. 1.5 - Prob. 1P Ch. 1.5 - Prob. 2P Ch. 1.5 - Prob. 3P Ch. 1.5 - Prob. 4P Ch. 1.5 - Prob. 5P Ch. 1.5 - Prob. 6P Ch. 1.5 - Prob. 7P Ch. 1.5 - Prob. 8P Ch. 1.5 - Prob. 9P Ch. 1.5 - Prob. 10P Ch. 1.5 - Prob. 11P Ch. 1.5 - Prob. 12P Ch. 1.5 - Prob. 13P Ch. 1.5 - Prob. 14P Ch. 1.5 - Prob. 15P Ch. 1.5 - Prob. 16P Ch. 1.5 - Prob. 17P Ch. 1.5 - Prob. 18P Ch. 1.5 - Prob. 19P Ch. 1.5 - Prob. 20P Ch. 1.5 - Prob. 21P Ch. 1.5 - Prob. 22P Ch. 1.5 - Prob. 23P Ch. 1.5 - Prob. 24P Ch. 1.5 - Prob. 25P Ch. 1.5 - Prob. 26P Ch. 1.5 - Prob. 27P Ch. 1.5 - Prob. 28P Ch. 1.5 - Prob. 29P Ch. 1.5 - Prob. 30P Ch. 1.5 - Prob. 31P Ch. 1.5 - Prob. 32P Ch. 1.5 - Prob. 33P Ch. 1.5 - Prob. 34P Ch. 1.5 - Prob. 35P Ch. 1.5 - Prob. 36P Ch. 1.5 - Prob. 37P Ch. 1.5 - Prob. 38P Ch. 1.5 - Prob. 39P Ch. 1.5 - Prob. 40P Ch. 1.5 - Prob. 41P Ch. 1.5 - Prob. 42P Ch. 1.5 - Figure 1.5.7 shows a slope field and typical...Ch. 1.5 - Prob. 44P Ch. 1.5 - Prob. 45P Ch. 1.5 - Prob. 46P Ch. 1.6 - Prob. 1P Ch. 1.6 - Prob. 2P Ch. 1.6 - Prob. 3P Ch. 1.6 - Prob. 4P Ch. 1.6 - Prob. 5P Ch. 1.6 - Prob. 6P Ch. 1.6 - Prob. 7P Ch. 1.6 - Prob. 8P Ch. 1.6 - Prob. 9P Ch. 1.6 - Prob. 10P Ch. 1.6 - Prob. 11P Ch. 1.6 - Prob. 12P Ch. 1.6 - Prob. 13P Ch. 1.6 - Prob. 14P Ch. 1.6 - Prob. 15P Ch. 1.6 - Prob. 16P Ch. 1.6 - Prob. 17P Ch. 1.6 - Prob. 18P Ch. 1.6 - Prob. 19P Ch. 1.6 - Prob. 20P Ch. 1.6 - Prob. 21P Ch. 1.6 - Prob. 22P Ch. 1.6 - Prob. 23P Ch. 1.6 - Prob. 24P Ch. 1.6 - Prob. 25P Ch. 1.6 - Prob. 26P Ch. 1.6 - Prob. 27P Ch. 1.6 - Prob. 28P Ch. 1.6 - Prob. 29P Ch. 1.6 - Prob. 30P Ch. 1.6 - Prob. 31P Ch. 1.6 - Prob. 32P Ch. 1.6 - Prob. 33P Ch. 1.6 - Prob. 34P Ch. 1.6 - Prob. 35P Ch. 1.6 - Prob. 36P Ch. 1.6 - Prob. 37P Ch. 1.6 - Prob. 38P Ch. 1.6 - Prob. 39P Ch. 1.6 - Prob. 40P Ch. 1.6 - Prob. 41P Ch. 1.6 - Prob. 42P Ch. 1.6 - Prob. 43P Ch. 1.6 - Prob. 44P Ch. 1.6 - Prob. 45P Ch. 1.6 - Prob. 46P Ch. 1.6 - Prob. 47P Ch. 1.6 - Prob. 48P Ch. 1.6 - Prob. 49P Ch. 1.6 - Prob. 50P Ch. 1.6 - Prob. 51P Ch. 1.6 - Prob. 52P Ch. 1.6 - Prob. 53P Ch. 1.6 - Prob. 54P Ch. 1.6 - Prob. 55P Ch. 1.6 - Suppose that n0 and n1. Show that the substitution...Ch. 1.6 - Prob. 57P Ch. 1.6 - Prob. 58P Ch. 1.6 - Solve the differential equation dydx=xy1x+y+3 by...Ch. 1.6 - Prob. 60P Ch. 1.6 - Prob. 61P Ch. 1.6 - Prob. 62P Ch. 1.6 - Prob. 63P Ch. 1.6 - Prob. 64P Ch. 1.6 - Prob. 65P Ch. 1.6 - Prob. 66P Ch. 1.6 - Prob. 67P Ch. 1.6 - Prob. 68P Ch. 1.6 - Prob. 69P Ch. 1.6 - As in the text discussion, suppose that an...Ch. 1.6 - Prob. 71P Ch. 1.6 - Prob. 72P Ch. 1 - Prob. 1RP Ch. 1 - Prob. 2RP Ch. 1 - Prob. 3RP Ch. 1 - Prob. 4RP Ch. 1 - Prob. 5RP Ch. 1 - Prob. 6RP Ch. 1 - Prob. 7RP Ch. 1 - Prob. 8RP Ch. 1 - Prob. 9RP Ch. 1 - Prob. 10RP Ch. 1 - Prob. 11RP Ch. 1 - Prob. 12RP Ch. 1 - Prob. 13RP Ch. 1 - Prob. 14RP Ch. 1 - Prob. 15RP Ch. 1 - Prob. 16RP Ch. 1 - Prob. 17RP Ch. 1 - Prob. 18RP Ch. 1 - Prob. 19RP Ch. 1 - Prob. 20RP Ch. 1 - Prob. 21RP Ch. 1 - Prob. 22RP Ch. 1 - Prob. 23RP Ch. 1 - Prob. 24RP Ch. 1 - Prob. 25RP Ch. 1 - Prob. 26RP Ch. 1 - Prob. 27RP Ch. 1 - Prob. 28RP Ch. 1 - Prob. 29RP Ch. 1 - Prob. 30RP Ch. 1 - Prob. 31RP Ch. 1 - Prob. 32RP Ch. 1 - Prob. 33RP Ch. 1 - Prob. 34RP Ch. 1 - Prob. 35RP Ch. 1 - Prob. 36RP

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Program Description: Purpose of problem is to calculate the general solution of the differential equation 6 x y 3 + 2 y 4 + ( 9 x 2 y 2 + 8 x y 3 ) y ′ = 0 .

Solution Summary: The author explains the purpose of the problem, which is to calculate the general solution to the differential equation.

Concept explainers

Program Description: Purpose of problem is to calculate the general solution of the differential equation 6xy3+2y4+(9x2y2+8xy3)y′=0 .

Want to see the full answer?

Chapter 1 Solutions