Question: The Euler-Cauchy Equation A well-known linear second-order equation with variable coefficients is the Euler-Cauchy Equation3 Where a, b, c ( IR. and a of; 0.

The Euler-Cauchy Equation A well-known linear second-order equation with variable coefficients is the Euler-Cauchy Equation3

Where a, b, c ( IR. and a of; 0. Show by substituting y = tr that solutions of this form are obtained when r is a solution of the Euler-Cauchy characteristic equation

Then verify that if r1 and r2 are distinct solutions o f (15), the general solution of (14) is given by

For arbitrary c1, c2 ( R?

arir-l) + br + c = 0.

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