Chapter 5.7, Problem 13E

(a)

To determine

To prove: The equation $y=e^{6x}$ is a solution of differential equation $y\text{'}\text{'}-y\text{'}-30y=0$.

(b)

To determine

To prove: The equation $y=e^{-5x}$ is a solution of differential equation $y\text{'}\text{'}-y\text{'}-30y=0$.

(c)

To determine

To prove: The equation $y=C_1{e}^{6x}+C_2{e}^{-5x}$ is a solution of differential equation $y\text{'}\text{'}-y\text{'}-30y=0$.