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
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
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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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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