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Thanks for any help and I hope I got myself clear

- Thread starter student85
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- #1

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Thanks for any help and I hope I got myself clear

- #2

HallsofIvy

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However, the first use of "homogeneous" applies only to

A first order differential equation that was "homogeneous" in the second sense would have to be of the form dy/dx= f(x)y and would be a relatively simple separable equation.

- #3

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...but wait, you said that an equation that would satisfy both definitions would be of the form dy/dx= f(x)y , but wouldn't it depend on f(x) to whether it satisfies the first definition(in which all terms are of the same degree)?

dy/dx has 0 degree right? y has a degree of 1, so f(x) would require a degree of -1 for the eq. to be homogeneous according to our first definition...or am I missing something?

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HallsofIvy

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