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Consider the second-order homogeneous linear equation y''−6y'+9y=0. (a) Use the substitution y=e^(rt) to attempt to find...

Consider the second-order homogeneous linear equation y''−6y'+9y=0.

(a) Use the substitution y=e^(rt) to attempt to find two linearly independent solutions to the given equation.

(b) Explain why your work in (a) only results in one linearly independent solution, y1(t).

(c) Verify by direct substitution that y2=te^(3t) is a solution to y''−6y'+9y=0. Explain why this function is linearly independent from y1 found in (a).

(d) State the general solution to the given equation

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