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Find the determinant. x² -Ed 2x 5x4 W(x5, x²) = = (x²)(5x4) - (2x)(x5) The Wronskian ---Select--- equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions ---Select--- linearly independent. Submit Skip (you cannot come back)

Find the determinant. x² -Ed 2x 5x4 W(x5, x²) = = (x²)(5x4) - (2x)(x5) The Wronskian ---Select--- equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions ---Select--- linearly independent. Submit Skip (you cannot come back)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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N? We are given the following homogenous differential equation and pair of solutions on the given interval. x²y" - 6xy' +10y = 0; x², x5, (0,00) We are asked to verify that the solutions are linearly independent. That is, there do not exist constants c₁ and c₂, not both zero, such that c₁x² + ₂x³ = 0. While this may be clear for these solutions that are different powers of x, we have a formal test to verify the linear independence. Recall the definition of the Wronskian for the case of two functions f, and f₂, each of which have a first derivative. W(f₁, f₂) = W(x², x5)= By Theorem 4.1.3, if W(f₁, f₂) = 0 for every x in the interval of the solution, then solutions are linearly independent. Let f₁(x) = x² and f₂(x) = x³. Complete the Wronskian for these functions. f₁ f₂ 2x 5x4 5.4
Transcribed Image Text:N? We are given the following homogenous differential equation and pair of solutions on the given interval. x²y" - 6xy' +10y = 0; x², x5, (0,00) We are asked to verify that the solutions are linearly independent. That is, there do not exist constants c₁ and c₂, not both zero, such that c₁x² + ₂x³ = 0. While this may be clear for these solutions that are different powers of x, we have a formal test to verify the linear independence. Recall the definition of the Wronskian for the case of two functions f, and f₂, each of which have a first derivative. W(f₁, f₂) = W(x², x5)= By Theorem 4.1.3, if W(f₁, f₂) = 0 for every x in the interval of the solution, then solutions are linearly independent. Let f₁(x) = x² and f₂(x) = x³. Complete the Wronskian for these functions. f₁ f₂ 2x 5x4 5.4
ON? Step 2 Find the determinant. W(x5, x²) = x5 2 2x 5x4 = (x²)(5x4) (2x)(x5) The Wronskian ---Select--- equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions ---Select--- linearly independent. Submit Skip (you cannot come back)
Transcribed Image Text:ON? Step 2 Find the determinant. W(x5, x²) = x5 2 2x 5x4 = (x²)(5x4) (2x)(x5) The Wronskian ---Select--- equal to 0 for every x in the interval (0, ∞o), therefore the set of solutions ---Select--- linearly independent. Submit Skip (you cannot come back)
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