Given that yet is a solution to the y5y5y11y0 differential e

Given that y\'=e^t is a solution to the y\'\'\'+5y\'\'+5y\'-11y=0 differential equation, find its general solution.

Using synthetic division
1 1 5 5 -11
1 6 11
1 6 11 0

x^2 +6x +11 is a characteristic equation
x= [-6 ±(36-44)]/2

x= -3 ± i2

So a general solution is

y(t)= C₁e^t +e^(-3t) (C₂ cos 2 t +C₃ sin2 t)

$Given that y\'=e^t is a solution to the y\'\'\'+5y\'\'+5y\'-11y=0 differential equation, find its general solution.SolutionUsing synthetic division 1 1 5 5 -11$

Given that yet is a solution to the y5y5y11y0 differential e

Solution

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