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Solve the subsequent IVP.
y′′ + 11y′ + 24 y = 0
y (0) =0
y′ (0)=-7
Solution
The characteristic equation is as
r2 +11r + 24 = 0
( r + 8) ( r + 3) = 0
Its roots are r1 = - 8 and r2 = -3 and then the general solution and its derivative is.
y (t ) = ce-8t + c e-3t
y′ (t ) = -8c1e -8t - 3c2e -3t
Here, plug in the initial conditions to find the subsequent system of equations.
0 = y (0) = c1 + c2
-7 = y′ (0) = -8c1 - 3c2
Solving this system provides c1 = 7and c2 = - 7. The actual solution to the differential equation is so y (t ) = (7/5) e-8t - (7/5) e-3t
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