Mathematics, 29.08.2020 01:01 ninaaforever

Consider the first order differential equation y′ + t/t2 − 25y = et/t − 9
For each of the initial conditions below, determine the largest interval a a. y(-7) = 6.4.
b. y(-2. 5) = -0.5.
c. y(0) = 0.
d. y(4.5) = -2.1.
e. y(14)= 1.7.

Answers: 3

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Answer from: drandbone92

For y(-7) =6.4

The largest interval is between

$-\infty \to -5$

For y(-2.5) = -0.5.

The largest interval is between

$-5 \to 5$

For y(0) = 0

The largest interval is between

$-5 \to 5$

For y(4.5) = -2.1.

The largest interval is between

$-5 \to 5$

For y(14)= 1.7.

The largest interval is between

$9 \to \infty$

Step-by-step explanation:

From m the question we are told that

The first order differential equation is $\frac{y' - t}{ t^2 -25} = \frac{e^t}{t-9}$

Now the first step is to obtain the domain of the differential equation

Now to do that let consider the denominators

Now generally

$t^2 - 25 \ne 0$ side calculation

=> $t\ne \pm5$ t^2 - 25 = 0

$t = \pm 5$

Also $t-9\ne 0$ t -9 = 0

=> $t\ne 9$ t= 9

This means that this first order differential equation is discontinuous at

$t = -5 , \ \ t = 5 \ \ t = 9$

$This \ is \ illustrated \ below \ \\ ------------------\\\. \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ |\\. \ -5 \ \ \ \ \ \ \ \ \ \ \ \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ 9$

For y(-7) =6.4

The largest interval is between

$-\infty \to -5$

For y(-2.5) = -0.5.

The largest interval is between

$-5 \to 5$

For y(0) = 0

The largest interval is between

$-5 \to 5$

For y(4.5) = -2.1.

The largest interval is between

$-5 \to 5$

For y(14)= 1.7.

The largest interval is between

$9 \to \infty$

Answer from: Quest

step-by-step explanation:

Answer from: Quest

the answer to question 1 is -8, 28.

step-by-step explanation:

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