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).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

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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, 00).

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