3 years ago

Suppose y varies inversely with x and y=20 when x=5. Write an equation for the inverse variation.

Mathematics

1 answer:

Viktor [21]3 years ago

4 0

K = 20 • 5 or 20 = k/5

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elena-s [515]

Answer:

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Step-by-step explanation:

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2 years ago

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Solve the differential equation dy/dx+4xy=x

Irina-Kira [14]

$\dfrac{\mathrm dy}{\mathrm dx}+4xy=x$
$\dfrac{\mathrm dy}{\mathrm dx}=x(1-4y)$

This ODE is separable, so you can write

$\dfrac{\mathrm dy}{1-4y}=x\,\mathrm dx$

Integrating both sides gives

$-\dfrac14\ln|1-4y|=\dfrac12x^2+C$
$\ln|1-4y|=-2x^2+C$
$1-4y=e^{-2x^2+C}$
$1-4y=Ce^{-2x^2}$
$y=\dfrac{1-Ce^{-2x^2}}4$