Given the Euler differential equation x²y" - 3xy' + 3y = 0 find the solution y(x) for x > 0, for the initial value problem y(1) = 20, y' (1) = 0. In your answer, provide the exponents of the functions x" appearing in the solution in increasing order (r₁ < 2) and the actual solution which is a polynomial having integer coefficients.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 5E
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Given the Euler differential equation
x²y" - 3xy' + 3y = 0
find the solution y(x) for x > 0, for the initial value problem y(1) = 20, y'(1) = 0.
In your answer, provide the exponents of the functions x" appearing in the solution
in increasing order (r₁ < 2) and the actual solution which is a polynomial having
integer coefficients.
Transcribed Image Text:Given the Euler differential equation x²y" - 3xy' + 3y = 0 find the solution y(x) for x > 0, for the initial value problem y(1) = 20, y'(1) = 0. In your answer, provide the exponents of the functions x" appearing in the solution in increasing order (r₁ < 2) and the actual solution which is a polynomial having integer coefficients.
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