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Anarel [89]
3 years ago
15

Find the general solution of the given differential equation. 5 dy dx + 45y = 9 y(x) = Give the largest interval I over which th

e general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) Determine whether there are any transient terms in the general solution.
Mathematics
1 answer:
Ahat [919]3 years ago
3 0

Answer:

Step-by-step explanation:

Given that the differential equation is:

5 \dfrac{dy}{dx}+ 45 y = 9\\

by dividing both sides by 5; we have:

\dfrac{dy}{dx}+ 9y = \dfrac{9}{5} --- (1)

which is a form of a linear equation.

The integrating factor is:

\mu = e^{\int}^{9dx }

\mu = e^{9x }

multiplying eqution (1) with \mu = e^{9x }

e^{9x}(\dfrac{dy}{dx}+ 9y)= (\dfrac{9}{5})e^{9x}

\dfrac{d}{dx}(ye^{9x})= (\dfrac{9}{5})e^{9x}

Using integration on both sides.

\int \dfrac{d}{dx}(ye^{9x}) dx= \int \dfrac{9}{5} e^{9x} \ dx

ye^{9x}=\dfrac{9}{5} \dfrac{e^{9x}}{9}+C

ye^{9x}= \dfrac{e^{9x}}{5}+C

y= \dfrac{1}{5}+Ce^{-9x}

Thus, the general solution is : y= \dfrac{1}{5}+Ce^{-9x} ; -\infty < x < \infty

In general solution:

y_c = ce^{-9x} \ and \ y_p = \dfrac{1}{5}

To talk of larger values of x, the value of y_c(x) is said to be negligible.

This implies that:

y_c  \to 0  \ as \  x \to \infty

Thus,

y_c (x) = ce ^{-9x} signifies a transient term in the general solution.

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The ratio of savings to expenditure is 2:8 find the savings if the expenditure is 24,000​
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the savings is 6000

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Below is the graph of y=x^3. <br> Translate it to make it the graph of y=(x-4)^3-1
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Answer:7=0.5 |x-4| -3

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20=|x-4|

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The answers are -16=x and 24=x

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Answer:

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