Solution to the equation y'' - y' - 6y = 0

Certainly, let's focus on solving the differential equation y'' - y' - 6y = 0 step by step without much theory. Step 1: Write down the differential equation: y'' - y' - 6y = 0 Step 2: Find the characteristic equation by assuming a solution of the form y(t) = e^(mt): m^2 - m - 6 = 0 Step 3: Solve the characteristic equation for m: m = 3 or m = -2 Step 4: Write down the general solution: y(t) = C1 * e^(3t) + C2 * e^(-2t) Here, C1 and C2 are arbitrary constants that depend on initial or boundary conditions.