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,

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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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= 5 37 A 4 8 0.5 06 9

For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Month Number (Thousands)Dec 1991 65.60Jan 1992 71.60Feb 1992 78.80Mar 1992 111.60Apr 1992 107.60May 1992 115.20Jun 1992 117.80Jul 1992 106.20Aug 1992 109.90Sep 1992 106.00Oct 1992 111.80Nov 1992 84.50Dec 1992 78.60Jan 1993 70.50Feb 1993 74.60Mar 1993 95.50Apr 1993 117.80May 1993 120.90Jun 1993 128.50Jul 1993 115.30Aug 1993 121.80Sep 1993 118.50Oct 1993 123.30Nov 1993 102.30Dec 1993 98.70Jan 1994 76.20Feb 1994 83.50Mar 1994 134.30Apr 1994 137.60May 1994 148.80Jun 1994 136.40Jul 1994 127.80Aug 1994 139.80Sep 1994 130.10Oct 1994 130.60Nov 1994 113.40Dec 1994 98.50Jan 1995 84.50Feb 1995 81.60Mar 1995 103.80Apr 1995 116.90May 1995 130.50Jun 1995 123.40Jul 1995 129.10Aug 1995…

For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Year Month Units1 Nov 42,1611 Dec 44,1862 Jan 42,2272 Feb 45,4222 Mar 54,0752 Apr 50,9262 May 53,5722 Jun 54,9202 Jul 54,4492 Aug 56,0792 Sep 52,1772 Oct 50,0872 Nov 48,5132 Dec 49,2783 Jan 48,1343 Feb 54,8873 Mar 61,0643 Apr 53,3503 May 59,4673 Jun 59,3703 Jul 55,0883 Aug 59,3493 Sep 54,4723 Oct 53,164

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Pearson eText Fundamentals of Differential Equations with Boundary Value Problems -- Instant Access (Pearson+)

Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 3E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 7E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...Ch. 11.2 - Prob. 9E Ch. 11.2 - In Problems 1-12, determine the solutions, if any,...

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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