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gizmo_the_mogwai [7]

3 years ago

10

5m+72=−2m+52 A -1 B -1/7 C 6/7 D 7

1 answer:

shtirl [24]3 years ago

5 0

<span>First we add 2m to both sides, leaving 7m + 72 = 52 (since -2m + 2m cancels out). Next, we subtract 72 from both sides, bringing us to 7m = -20. Solving for m, we get -20/7. Since this is not one of the listed options, it is possible that the original poster has made a typographical error.</span>

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Step-by-step explanation:

The given differential equation is

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It can be written as

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Integrate both sides.

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Apply ILATE rule on right side. Here, t is first function and $e^{-t}$ is the second function.

$y=t\int e^{-t}-\int (\frac{d}{dt}t\int e^{-t})$

$y=-te^{-t}-\int (1\times (-e^{-t}))$ $\int e^{-x}=-e^{-x}+C$

$y=-te^{-t}+\int e^{-t}$

$y=-te^{-t}-e^{-t}+C$ .... (1)

Initial condition is y(1) = 1. It means at t=1 the value of y is 1.

$1=-(1)e^{-t}-e^{-(1)}+C$

$1=-e^{-1}-e^{-1}+C$

$1=-2e^{-1}+C$

$1=-\frac{2}{e}+C$

Add $\frac{2}{e}$ on both sides.

$1+\frac{2}{e}=C$

Substitute the value of C in equation (1).

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Therefore, the solution of given initial value problem is $y=-e^{-t}(t+1)+1+\frac{2}{e}$ .

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