Show that y = Cerx is a solution of y + ay' + by = 0 if
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Show that y = Cerx is a solution of y" + ay' + by = 0 if and only if r is a root of P(r) = r2 + ar + b. Then verify directly that y = C1e3x + C2e−x is a solution of y" − 2y' − 3y = 0 for any constants C1,C2.
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