Explanation Given: The given condition is: d y d x = y ; y ( 0 ) = 1 Approach: Let y = f ( x ) be the solution of the differential equation: d y d x = g ( x , y ) , with y ( x 0 ) = y 0 For x 0 ≤ x ≤ x n , let x i + 1 = x i + h , where h = ( x n − x 0 ) n and, y i + 1 = y i + g ( x i , y i ) h For 0 ≤ i ≤ n − 1 . Then, f ( x i + 1 ) ≈ y i + 1 And, General solution of d y d x = p ( x ) q ( y ) : ∫ q ( y ) d y = ∫ p ( x ) d x Calculation: Consider the given differential equation: d y d x = y ; y ( 0 ) = 1 We can write as: g ( x , y ) = y Substitute the value 0 for x and 1 for y : g ( x 0 , y 0 ) = 1 and, y 1 = y 0 + g ( x 0 , y 0 ) h = 1 + 1 ( 0.2 ) = 1.2 Now, x 1 = 0.2 , y 1 = 1.2 then: g ( x 1 , y 1 ) = 1.2 and, y 2 = y 1 + g ( x 1 , y 1 ) h = 1.2 + 1.2 ( 0.2 ) = 1.44 Now, find the function using variable separable, we get: ∫ 1 y d y = ∫ d x ln y = x + c y = k e x Substitute the value 0 for x and 1 for y :

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 11.3, Problem 28E

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The solution for the given condition dydx=y; y(0)=1 and also graph the solution.

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Chapter 11.3, Problem 27E

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The solution for the given condition d y d x = y ; y ( 0 ) = 1 and also graph the solution.

Solution Summary: The author explains how to find the solution for the given condition and graph it.

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To find:

The solution for the given condition dydx=y; y(0)=1 and also graph the solution.

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Chapter 11 Solutions

The solution for the given condition d y d x = y ; y ( 0 ) = 1 and also graph the solution.

Solution Summary: The author explains how to find the solution for the given condition and graph it.

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To find: The solution for the given condition dydx=y; y(0)=1 and also graph the solution.

Want to see the full answer?

Chapter 11 Solutions

To find:

The solution for the given condition dydx=y; y(0)=1 and also graph the solution.