4. Make up an ODE with desired solutions: a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following equation by the method of Frobenius, and show that you do indeed obtain those solutions. (x²-x)y "+(4x-2)y '+2y=0 (0 < x <1) b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and G(x).
4. Make up an ODE with desired solutions: a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following equation by the method of Frobenius, and show that you do indeed obtain those solutions. (x²-x)y "+(4x-2)y '+2y=0 (0 < x <1) b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and G(x).
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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Transcribed Image Text:4. Make up an ODE with desired solutions:
a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following
equation by the method of Frobenius, and show that you do indeed obtain those solutions.
(x²-x)y "+(4x-2)y '+2y=0
(0 < x <1)
b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and
G(x).
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