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Q. 27

Found in: Page 570


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.


Ans: The solution of the differential equation dydx=xey is y=ln12x2+C

See the step by step solution

Step by Step Solution

Step 1. Given information.



Step 2. Consider the differential equation defined by equation (1) given below and solve it by using antidifferentiation and/or separation of the variable method.  

dydx=xe-y ....(1)

Step 3. Solution

Note that the differential equation (1) is of the form of dydx=p(x)q(y) in which p(x)=x and q(y)=e-y. So the differential equation can be solved by applying the variable separable method. Separate the variables and integrate both the sides


Hence a solution to the differential equation dydx=xe-y isrole="math" localid="1649178838912" y=ln12x2+C

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