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enot [183]
2 years ago
13

Solve the following ODE's: c) y* - 9y' + 18y = t^2

Mathematics
1 answer:
Nastasia [14]2 years ago
7 0

Answer:

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = C_1e^{3t}+C_2e^{6t}

now calculating P.I.

P.I. = \frac{t^2}{D^2 - 9D +18}

P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

hence the complete solution

y = C.F. + P.I.

y = C_1e^{3t}+C_2e^{6t} + \dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})

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tester [92]

Answer:

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so the answer would be 37 1/8 I think

hope this helped

7 0
2 years ago
15 Points Help Math question
gizmo_the_mogwai [7]
11.11111111

you can round your answer

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3 0
3 years ago
13. Janine has job offers at two companies. One
Firdavs [7]

9514 1404 393

Answer:

  • 13 years
  • $62,000

Step-by-step explanation:

a) The 36000 -23000 = 13000 difference in salary is being made up at the rate of 3000 -2000 = 1000 per year. It will take 13000/1000 = 13 years for the salaries to be the same.

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b) After 13 years, the salary will be ...

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4 0
2 years ago
Read 2 more answers
Jules is measuring a patient’s height at 4 feet What is this height in inches? Answer
kondor19780726 [428]

Answer:

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3 0
2 years ago
Courtney is twice as old as Andre and three years older than Natalie. Courtney is half Shari's age. The difference between Shari
lesantik [10]

The question does not seem complete, but I'll represent the statement mathematically and look for their ages each. This is because the worst they can ask for is their ages.

Let C stand for Courtney's age, A for Andrei's age, N for Natalie's age and S for Shari's age. From the question we can deduce the following:

C = 2A

C = N + 3

C = S/2

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C + 3 = C + C/2

C/2 = 3 and C = 6

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A = 3

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N = 6 - 3

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S = 2C

S = 2 x 6

S = 12.

C = 6, A = 3, N = 3 and S = 12

8 0
2 years ago
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