MAT244--2019F > Quiz-4

Quiz 4 (TUT0601)

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etheliachoi:
Find the general solution of this equation:

y''+y'-6y = 12e3t+12e-2t

Find the homogenous solution:

y''+y'-6y=0
r2+r-6r=0
(r+3)(r-2)=0
r1 = -3, r2 = 2
y1(t)= e-3t, y2(t)= e2t
Then,
y(t) =c1e-3t + c2e2t
Now, consider
y''+y'-6y = 12e3t
Want to find:
Y(t) = Ae3t
Y'(t) = 3Ae3t, Y''(t) = 9Ae3t
Then,
9Ae3t + 3Ae3t - 6Ae3t = 12e3t
Thus, solving the equation, we get that:
A = 2 and Y(t) = 2e3t
Now, consider
y''+y'-6y = 12e-2t
Want to find:
Y(t) = Be-2t
Repeat for the process for Y(t) and solve for B. Hence, we get that
B = -3 and Y(t) = -3e-2t
Lastly,
y = c1e-3t + c2e2t + 2e3t - 3e-2t

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