(b) Consider yı and y2 as two solutions for the following DE where yı = x-1 and the Wronskian of the solutions is W (y1, Y2) = e*. Find p(x) and q(x) and write the DE. y" + p(x) y' + q(x) y = 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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Solve b

(a) Determine if the following sets of functions are linearly dependent or linearly independent on
IR.
-x¸ -2e2a + 5e¬ª
-x
(ii) x|x|, x?
(b) Consider
of the solutions is W (y1, Y2) = e². Find p(x) and q(x) and write the DE.
Y1
and
Y2 as two solutions for the following DE where y1 = x-1 and the Wronskian
y" + p(x) y' + q(x) y = 0
Transcribed Image Text:(a) Determine if the following sets of functions are linearly dependent or linearly independent on IR. -x¸ -2e2a + 5e¬ª -x (ii) x|x|, x? (b) Consider of the solutions is W (y1, Y2) = e². Find p(x) and q(x) and write the DE. Y1 and Y2 as two solutions for the following DE where y1 = x-1 and the Wronskian y" + p(x) y' + q(x) y = 0
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