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Separable differential equations Find the general solution

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Problem 24E Chapter 7.8

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 24E

Separable differential equations Find the general solution of the following equations.

, where y > 0

Step-by-Step Solution:
Step 1 of 3

Problem 24E

Separable differential equations Find the general solution of the following equations.

, where y > 0

Answer;

    Step-1;

                 DEFINITION : A differential equation is said to be of type “variable separable” if it can be expressed in such  a way , so that the coefficient of  dx is a function of of x alone and the coefficient of dy is a function of y alone.

       The general form of such differential  equation can be written as

                         

                                          f(x) dx = g(y)dy ……………….(1)

   Integrating both sides and adding an arbitrary constant C , we get the general solution as

                                              f(x)dx = +C

Working  rule of solving by the method of separation of variables;

Write the  given  differential equation in the form

                                                    f(x) dx = g(y)dy

          That is make the coefficient of dx as an expression of x alone and that of dy as an expression of y alone

    2. Integrate  both sides and add an arbitrary constant to any one side and get the general solution.

Step-2;

             In this problem we have to check whether the given equation is separable or not and if they are separable we have to solve the given initial value problem.

                     Given equation is ;  = y (+1) , where y >0

                                                   dy = (………………(2)

                From (1) , it is in the form of  f( x) dx  = g(y) dy, where f(x) = , and g(y) =  .

      That is ,  the coefficient of  dx is a function of of   ‘x’ alone and the coefficient of dy is a function of ‘y’ alone.

                      Thus , by the definition the given equation is separable.

                       ...

Step 2 of 3

Chapter 7.8, Problem 24E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Since the solution to 24E from 7.8 chapter was answered, more than 241 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: equations, general, Find, Differential, separable. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Separable differential equations Find the general solution of the following equations. , where y > 0” is broken down into a number of easy to follow steps, and 16 words. The full step-by-step solution to problem: 24E from chapter: 7.8 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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