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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the

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1 answer:

crimeas [40]2 years ago

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Answer:

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Step-by-step explanation:

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cupoosta [38]

It looks like you're asked to find the value of y(-1) given its implicit derivative,

$\dfrac{dy}{dx} = y^4$

and with initial condition y(2) = -1.

The differential equation is separable:

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Integrate both sides:

$\displaystyle \int \frac{dy}{y^4} = \int dx$

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Solve for y :

$\dfrac1{3y^3} = -x + C$

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$y^3 = -\dfrac1{3x+C}$

$y = -\dfrac1{\sqrt[3]{3x+C}}$

Use the initial condition to solve for C :

$y(2) = -1 \implies -1 = -\dfrac1{\sqrt[3]{3\times2+C}} \implies C = -5$

Then the particular solution to the differential equation is

$y(x) = -\dfrac1{\sqrt[3]{3x-5}}$

and so

$y(-1) = -\dfrac1{\sqrt[3]{3\times(-1)-5}} = \boxed{\dfrac12}$

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