Mathematics: [tex] rac{dx}{dt} = rac{t^{2}+3tx+ x^{2} }{ t^{2} } [/tex]

[tex] \frac{dx}{dt} = \frac{t^{2}+3tx+ x^{2} }{

Ответ:

AnhQNguyen6764

12.03.2022

$\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{t^2+3tx+x^2}{t^2}$
$\dfrac{\mathrm dx}{\mathrm dt}=1+\dfrac{3x}t+\dfrac{x^2}{t^2}$

Let x(t)=ty(t)

, so that $\dfrac{\mathrm dx}{\mathrm dt}=t\dfrac{\mathrm dy}{\mathrm dt}+y$ .

$t\dfrac{\mathrm dy}{\mathrm dt}+y=1+3y+y^2$
$t\dfrac{\mathrm dy}{\mathrm dt}=1+2y+y^2=(1+y)^2$
$\dfrac{\mathrm dy}{(1+y)^2}=\dfrac{\mathrm dt}t$
$\implies-\dfrac1{1+y}=\ln|t|+C$
$\implies y+1=-\dfrac1{\ln|t|+C}$
$\implies yt=x=-t-\dfrac t{\ln|t|+C}$

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Ответ:

blythephillips2734

02.06.2023

Mathematics

The measure of center and range to be used to compare the population is the median and the inter quartile range.

Explanation:

You utilize the median and the interquartile range (IQR) to portray skewed distributions of information. To look at two populaces, utilize the mean and the MAD when the two populations are symmetric. Utilize the middle and the IQR when possibly one or the two circulations are slanted.

In statistics and probability theory, the median is the worth isolating the higher half from the lower half of an information test, a populace or a likelihood circulation. For an informational collection, it might be thought of as the "center" esteem.

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$\frac{dx}{dt} = \frac{t^{2}+3tx+ x^{2} }{ t^{2} }$

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