Consider the functions fi(x) = 6x, f2(x) = 3x², and f3(x) = 12x + 3x². A) If fi and f2 are solutions of the DE x²y" – 2xy' + 2y = 0, show that f3(x) is also a solution for the DE. B) Use the Wronskian to show that fi,f2 and f3 are linearly dependent on the interval (-0, 0).
Consider the functions fi(x) = 6x, f2(x) = 3x², and f3(x) = 12x + 3x². A) If fi and f2 are solutions of the DE x²y" – 2xy' + 2y = 0, show that f3(x) is also a solution for the DE. B) Use the Wronskian to show that fi,f2 and f3 are linearly dependent on the interval (-0, 0).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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