To determine To solve: The resulting differential equation y d y + ( y − 2 x 2 ) d x = x d x . Explanation Procedure used: “A differential equation of the first order and first degree contains the first derivative to the first power. That is, it may be written as d y d x = f ( x , y ) . This type of equation is more commonly expressed in its differential for M ( x , y ) d x + N ( x , y ) d y = 0 . Where M ( x , y ) and N ( x , y ) represent constants, functions of either x or y , or functions of x and y . To solve an equation of the form of equation, first integrate. However, if M ( x , y ) contains y , the first term cannot be integrated. Also, if N ( x , y ) contains x , the second term cannot be integrated. If it is possible to rewrite equation as A ( x ) d x + B ( y ) d y = 0 where A ( x ) does not contain y and B ( y ) does not contain x , then find the solution by integrating each term and adding the constant of integration . ” Formula used: Combinations of differentials 2 ( x d x + y d y ) = d ( x 2 + y 2 ) . Calculation: The given differential equation is y d y + ( y − 2 x 2 ) d x = x d x . y d y + ( y − 2 x 2 ) d x = x d x y d y − x d x + ( y − 2 x 2 ) d x = 0 Now divide by ( y − 2 x 2 ) in both sides of obtained equation

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 31.3, Problem 15E

To determine

To solve: The resulting differential equation ydy+(y−2x2)dx=xdx.

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Chapter 31.3, Problem 14E

Chapter 31.3, Problem 16E

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Chapter 31 Solutions

Basic Technical Mathematics

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

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