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Solution to the equation y'' - y' - 6y = 0
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Answer to a math question Solution to the equation y'' - y' - 6y = 0
Clarabelle
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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.
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