Explanation Given information: The provided initial value problem y e x d y = ( y 2 + 2 y + 2 ) d x and the initial point is ( 0 , − 1 ) . Concept used: The differential equation of the form, d y d x = g ( x ) f ( y ) is said to be separable. And we solve it by separating variables. The general solution is given by, ∫ f ( y ) d y = ∫ g ( x ) d x . Consider the provided differential equation y e x d y = ( y 2 + 2 y + 2 ) d x . The above differential equation can be written as, y e x d y = ( y 2 + 2 y + 2 ) d x y d y ( y 2 + 2 y + 2 ) = d x e x So, the provided equation y e x d y = ( y 2 + 2 y + 2 ) d x is separable. Now integrate on both sides, ∫ y d y ( y 2 + 2 y + 2 ) = ∫ d x e x ∫ y d y ( y + 1 ) 2 + 1 = ∫ d x e x 1 2 ln | y 2 + 2 y +

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 14.1, Problem 51PS

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To calculate: The solution of the initial value problem yexdy=(y2+2y+2)dx for x=0 and y=−1 .

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Chapter 14.1, Problem 50PS

Chapter 14.1, Problem 52PS

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The solution of the initial value problem y e x d y = ( y 2 + 2 y + 2 ) d x for x = 0 and y = − 1 .

Solution Summary: The author explains the solution of the initial value problem yexdy=left, which is separable and solves by separating variables.

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To calculate: The solution of the initial value problem yexdy=(y2+2y+2)dx for x=0 and y=−1 .

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Chapter 14 Solutions