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Pavel [41]
3 years ago
6

Suppose x=c1e−t+c2e3tx=c1e−t+c2e3t. Verify that x=c1e−t+c2e3tx=c1e−t+c2e3t is a solution to x′′−2x′−3x=0x′′−2x′−3x=0 by substitu

ting it into the differential equation. (Enter the terms in the order given. Enter c1c1 as c1 and c2c2 as c2.)
Mathematics
1 answer:
Harrizon [31]3 years ago
4 0

The correct question is:

Suppose x = c1e^(-t) + c2e^(3t) a solution to x''- 2x - 3x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c1 as c1 and c2 as c2.)

Answer:

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

Step-by-step explanation:

We need to verify that

x = c1e^(-t) + c2e^(3t)

is a solution to the differential equation

x''- 2x' - 3x = 0

We differentiate

x = c1e^(-t) + c2e^(3t)

twice in succession, and substitute the values of x, x', and x'' into the differential equation

x''- 2x' - 3x = 0

and see if it is satisfied.

Let us do that.

x = c1e^(-t) + c2e^(3t)

x' = -c1e^(-t) + 3c2e^(3t)

x'' = c1e^(-t) + 9c2e^(3t)

Now,

x''- 2x' - 3x = [c1e^(-t) + 9c2e^(3t)] - 2[-c1e^(-t) + 3c2e^(3t)] - 3[c1e^(-t) + c2e^(3t)]

= (1 + 2 - 3)c1e^(-t) + (9 - 6 - 3)c2e^(3t)

= 0

Therefore, the differential equation is satisfied, and hence, x is a solution.

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4 0
3 years ago
The number of miles that Jenna cycled each week for a 7-week period is shown: 36, 42, 28, 52, 48, 36, 31 What is the median numb
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Answer:

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Step-by-step explanation:

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The median it therefore = 36

7 0
3 years ago
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For parallelogram ABCD, find the value of x.<br> 3x + 20<br> B<br> С<br> A А<br> D<br> 5x – 12
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Answer:

x = 16

Step-by-step explanation:

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An angle measures 18.6° less than the measure of its complementary angle. What is the measure of each angle?
weeeeeb [17]

Answer:

X = 35.7 Y=54.3

Step-by-step explanation:

Let the 2 angles be called X and Y were X is the smaller angle

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6 0
2 years ago
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