Explanation Given: The differential equation is, d d x ( ( 1 + x ) d y d x ) + e − x y + λ y = 0 Approach: Sturm-Lioville problem: d d x ( p d y d x ) + q y + λ r y = 0 , a < x < b , … ( 1 ) Here, p , p ′ , q , and r are continuous on [ a , b ] and p and r are positive on [ a , b ] Let ϕ be a nontrivial solution of Equation ( 1 ) with consecutive zeros x 1 and x 2 in [ a , b ] and λ > max { − q M r M , − q m r m , 0 } , then the distance between the zeroes x 1 and x 2 is bounded by π p m q M + λ r M ≤ x 2 − x 1 ≤ π p M q m + λ r m … ( A ) Calculation: The problem is given by, d d x ( ( 1 + x ) d y d x ) + e − x y + λ y = 0 ... ( 2 ) This is a Sturm Lioville problem. Compare Equation ( 2 ) and Equation ( 1 ) Then, p = 1 + x q = e − x r = 1 So,

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 11.8, Problem 11E

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The estimated distance between consecutive zeros in [0,5] of a nontrivial solution to ddx((1+x)dydx)+e−xy+λy=0.

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Chapter 11.8, Problem 10E

Chapter 11.8, Problem 12E

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The estimated distance between consecutive zeros in [ 0 , 5 ] of a nontrivial solution to d d x ( ( 1 + x ) d y d x ) + e − x y + λ y = 0 .

Solution Summary: The author explains that the distance between consecutive zeros in left[0,5right] of a nontrivial solution to

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The estimated distance between consecutive zeros in [0,5] of a nontrivial solution to ddx((1+x)dydx)+e−xy+λy=0.

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Chapter 11 Solutions