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2 years ago

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

Mathematics

1 answer:

Misha Larkins [42]2 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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2 years ago

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Dennis_Churaev [7]

Answer:

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Step-by-step explanation:

so we are going to take the original coordinates (-5,1) and to the operation that the question wants us to do (x-4,y+3) by subsitituing the variables in so we get (-5-4,1+3)

Answer: (-9,4)

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1 year ago

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2 years ago

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