2 years ago

Which number line represents thedata

Mathematics

1 answer:

butalik [34]2 years ago

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Did you forget to attach an image

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Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x , with ini

Svetach [21]

For this case we have the following difference equation:
$dy / dx = 3xy
$
Applying separable variables we have:
$dy / y = 3xdx
$
Integrating both sides we have:
$\int\ ({1/y}) \, dy = \int\ {3x} \, dx$
$ln (y) = (3/2) x ^ 2 + C
$
applying exponential to both sides:
$exp (ln (y)) = exp ((3/2) x ^ 2 + C)

 y = C * exp ((3/2) x ^ 2)$
For y (1) = 1 we have:
$C = 1 / (exp ((3/2) * 1 ^ 2))

C = 0.2$
Thus, the particular solution is:
$y = 0.2 * exp ((3/2) x ^ 2)
$
Whose domain is all real.
Answer:
y = 0.2 * exp ((3/2) x ^ 2)
Domain: all real numbers

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Afina-wow [57]

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