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Consider the initial value problem: x²y" + 6y = 4.xy' + 12 y(0) = 2, y'(0) = 0 a) Show that y=x^3 + 2 is a solution to this initial value problem. b)Show that y=x^2+ 2 is a solution to this initial value problem. c)Explain why parts (a)/(b) do NOT contradict the Existence and Uniqueness Theorem for linear Differential Equations.

Consider the initial value problem: x²y" + 6y = 4.xy' + 12 y(0) = 2, y'(0) = 0 a) Show that y=x^3 + 2 is a solution to this initial value problem. b)Show that y=x^2+ 2 is a solution to this initial value problem. c)Explain why parts (a)/(b) do NOT contradict the Existence and Uniqueness Theorem for linear Differential Equations.

Advanced Engineering Mathematics
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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Consider the initial value problem: x²y" + 6y = 4xy' + 12 y(0) = 2, y'(0) = 0 %D a) Show that y=x^3 + 2 is a solution to this initial value problem. b)Show that y=x^2+ 2 is a solution to this initial value problem. c)Explain why parts (a)/(b) do NOT contradict the Existence and Uniqueness Theorem for linear Differential Equations.
Transcribed Image Text:Consider the initial value problem: x²y" + 6y = 4xy' + 12 y(0) = 2, y'(0) = 0 %D a) Show that y=x^3 + 2 is a solution to this initial value problem. b)Show that y=x^2+ 2 is a solution to this initial value problem. c)Explain why parts (a)/(b) do NOT contradict the Existence and Uniqueness Theorem for linear Differential Equations.
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