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3 years ago

Please help me please

Mathematics

1 answer:

kobusy [5.1K]3 years ago

7 0

Terrell ran 1,000 meters more than Victor. That's the answer because if you know 1 kilometer = 1,000 meters than do 3 kilometers times 1 kilometer = 3,000 meters. Than do 4,000 meters -3,000 meters to get 1,000 meters. so the answer is Terrell ran 1,000 meters more than Victor.

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$w' x(\ln x)^2+(2\ln x+(\ln x)^2)w=0$

and noting that

$\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x$

we can write the ODE as

$\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0$

Integrating both sides with respect to $x$ , we get

$wx(\ln x)^2=C_1$
$w=\dfrac{C_1}{x(\ln x)^2}$

Now solve for $v$ :

$v'=\dfrac{C_1}{x(\ln x)^2}$
$v=-\dfrac{C_1}{\ln x}+C_2$

So you have

$y_2=v\ln x=-C_1+C_2\ln x$

and given that $y_1=\ln x$ , the second term in $y_2$ is already taken into account in the solution set, which means that $y_2=1$ , i.e. any constant solution is in the solution set.

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3 years ago