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creativ13 [48]
3 years ago
9

Find a general solution of y" + 8y' + 16y=0.

Mathematics
1 answer:
Misha Larkins [42]3 years ago
6 0

Answer:

The general solution: C_{1}e^{-4x} + xC_{2}e^{-4x}

Step-by-step explanation:

Differential equation: y'' + 8y' + 16y = 0

We have to find the general solution of the above differential equation.

The auxiliary equation for the above equation can be writtwn as:

m² + 8m +16 = 0

We solve the above equation for m.

(m+4)² = 0

m_{1} = -4, m_{2} = -4

Thus we have repeated roots for the auxiliary equation.

Thus, the general solution will be given by:

y = C_{1}e^{m_{1}x} + xC_{2}e^{m_{2}x}

y = C_{1}e^{-4x} + xC_{2}e^{-4x}

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Answer:

8% tax rate.

Step-by-step explanation:

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The 8% (0.08) is the tax rate because the 100%, or 1.00, is the original price of the racket, which was $13.

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