Homogeneous Linear Equations

Part a: Distinct Real Roots

Each differential equation has an associated characteristic equation with distinct real roots.

For example, an eqaution like

ay'' + by' + cy = 0

will have characteristic eqaution

ar^2 + br + c = 0

with factorization $ar^2 + br + c = a(r-d)(r-e)$ , where $d \neq e$ .

You must meet all initial conditions for the answer to be complete.

Please enter any multiplication explicitly with * symbols so the parcer can understand your answer, like this:

2t^3e^{5t^2} \longrightarrow 2*t^3*e^{(5*t^2)}.

Find a family of functions that solves the equation and satisfies the conditions below.

y'' -5y' + 6y = 0