2 years ago

The value of the 6 in the number 60,324 is how many times greater than the value of the 6 in the number 4,621

Mathematics

1 answer:

ehidna [41]2 years ago

6 0

100 hundred times larger

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As a Bernoulli equation:

$x^2\dfrac{\mathrm dy}{\mathrm dx}=6y^2+6xy\iff x^2y^{-2}\dfrac{\mathrm dy}{\mathrm dx}-6xy^{-1}=6$

Let $z=y^{-1}\implies\dfrac{\mathrm dz}{\mathrm dx}=-y^{-2}\dfrac{\mathrm dy}{\mathrm dx}$ . The ODE becomes

$-x^2\dfrac{\mathrm dz}{\mathrm dx}-6xz=6$
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With $y(3)=6$ , we get

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so the solution is

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which is valid as long as the denominator is not zero, which is the case for all $x\neq\sqrt[5]{\dfrac{4131}{12}}$ .

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2 years ago

The value of the 6 in the number 60,324 is how many times greater than the value of the 6 in the number 4,621​

The value of the 6 in the number 60,324 is how many times greater than the value of the 6 in the number 4,621