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## Homework Statement

Show that each function in the family satisfies the differential equation.

y(x) = x/(1+cx) ; dy/dx = y^2/x^2

## The Attempt at a Solution

I'm not sure where to start. I can't see how the integral of dy/dx = y(x)

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- Thread starter ziggie125
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- #1

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Show that each function in the family satisfies the differential equation.

y(x) = x/(1+cx) ; dy/dx = y^2/x^2

I'm not sure where to start. I can't see how the integral of dy/dx = y(x)

- #2

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Start by taking dy/dx of your y(x) equation, then compare that to y^2/x^2. What do you get?

- #3

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y(x) = x/(1+cx)

dy/dx = ((1+cx) - xc)/(1+cx)^2 = 1/(1+cx)^2

So how does that equal y^2/x^2

- #4

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What is y^2/x^2?

- #5

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I'm not sure what you mean. This is all the information i was given for the problem.

- #6

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- #7

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y^2/x^2 = 1/(1 cx)^2

y^2 = x^2/(1+cx)^2

sqrt(y^2) = sqrt(x^2/(1+cx)^2) = sqrt((x/(1+cx))^2))

y = x/(1+cx)

- #8

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- #9

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Alright. Thanks for the help, it is greatly appreciated.

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