A second-order Euler equation is one of the form where a, b, c are constants. (a) Show

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A second-order Euler equation is one of the form


image


where a, b, c are constants.


(a) Show that if x > 0, then the substitution v = ln x transforms Eq. (22) into the constant- coefficient linear equation


image


with independent variable v.


(b) If the roots r1 and r2 of the characteristic equation of Eq. (23) are real and distinct, conclude that a general solution of the Euler equation in (22) is y(x) = c1xr1 + c2xr2.

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Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

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