To determine The approximate solution of d y d x − x 2 y 2 = 1 with y ( 0 ) = 2 and h = 0.2 . Explanation Given: The differential equation is shown below. d y d x − x 2 y 2 = 1 The width h of the interval [ 0 , 1 ] is 0.2 and y ( 0 ) = 2 . Concept used: Consider the solution of the differential equation d y d x = g ( x , y ) be y = f ( x ) with y ( x 0 ) = y 0 for x 0 ≤ x ≤ x n . Consider x i + 1 = x i + h and the value of h is shown below. h = x n − x 0 n Then the value of y i + 1 is shown below. y i + 1 = y i + g ( x i , y i ) h … … ( 1 ) If 0 ≤ i ≤ n − 1 then the approximation is shown below. f ( x i + 1 ) ≈ y i + 1 Calculation: The given differential equation is shown below. d y d x − x 2 y 2 = 1 Rewrite the differential equation as follows: d y d x = 1 + x 2 y 2 The function g ( x , y ) is shown below. g ( x , y ) = 1 + x 2 y 2 … … ( 2 ) The value of x 0 = 0 and y 0 = 2 from the equation y ( x 0 ) = y 0 . To obtain the value of g ( x 0 , y 0 ) substitute 0 for x 0 and 2 for y 0 in equation (2) as follows: g ( x 0 , y 0 ) = 1 + 0 2 ( 2 ) 2 = 1 To obtain the value of y 1 , substitute 0 for i in equation (1) as follows: y 0 + 1 = y 0 + g ( x 0 , y 0 ) h y 1 = y 0 + g ( x 0 , y 0 ) h Substitute 2 for y 0 , 1 for g ( x 0 , y 0 ) and 0

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.3, Problem 1YT

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The approximate solution of dydx−x2y2=1 with y(0)=2 and h=0.2.

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Chapter 10.2, Problem 32E

Chapter 10.3, Problem 1E

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Chapter 10 Solutions

Calculus with Applications (11th Edition)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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