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Vlada [557]
3 years ago
9

Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist

. (Enter your answer using interval notation.) (t − 5)y' + (ln t)y = 6t, y(1) = 6
Mathematics
1 answer:
yuradex [85]3 years ago
3 0

Answer:

0 < t < 5 is the required interval for the differential equation (t - 5)y' + (ln t)y = 6t to have a solution.

Step-by-step explanation:

Given the differential equation

(t - 5)y' + (ln t)y = 6t

and the condition y(1) = 6

We can rewrite the differential equation by dividing it by (t - 5) as

y' + [(ln t)/(t - 5)]y = 6t/(t - 5)

(ln t)/(t - 5) is continuous on the interval (0, 5) and (5, +infinity).

6t/(t - 5) is continuous on (-infinity, 5) and (5, +infinity)

We see that for these expressions, we have continuity at the intervals (0, 5) and (5, +infinity).

But the initial condition is y = 6, when t = 1.

The solution to differential equation is certain to exist at (0, 5)

Which implies that

0 < t < 5

is the required interval.

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The answer is 3/4
Hope the answer helps :)
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Help me do examples for a function and a non function
bekas [8.4K]

Answer:

{(1,2) (3,4) (5,6)} and {(1,2) (1,4) (5,6)}

Step-by-step explanation:

you really want to think of a function as a vending machine. if you press B12 on a vending machine because thats where the chips are, only the chips should come out. in a function, the input value aka x (B12, what youre putting in) should only have one output value aka y, (the chips)

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an important thing to remember is that one output value can belong to multiple input values. there can be chips (output) in both B12 and C12 (inputs) BUT as i said before, there CANNOT be two outputs for one input. B12 cannot give you both chips and a drink.

using this, another example of a function would be {(1,2) (3,2) (5,2)}

an example of an non function would be {(1,2) (1,4) (5,6)} because x, the input value, has multiple output values which is not possible. the output of 1 can not be 2 and 4 at the same time which we can see in the (x,y) coordinates.

4 0
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If you add up all of the money James has earned, (1 + 7 + 14), it equals 22. If you subtract 22 from 100, it equals 78. Therefore James needs to earn 78 more dollars.

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2 years ago
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