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March 21st, 2019, 04:26 AM   #1
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Help classifying DEs

I need help classifying the following differential equations as:

- linear
- Bernoulli equation
- separable
- exact
- homogeneous
- both linear and exact
- both linear and separable
- both Bernoulli and separable

a) $\displaystyle dy/dx = y^2/x^2 - x/y$ (My answer: homogeneous)

b) $\displaystyle dy/dx = x/y - 2. y^3/x^3$ (My answer: homogeneous)

c) $\displaystyle (3x^2 - 2y^2 - ½\cdot y\cdot\cos x) dx + (-4xy - ½\cdot\sin x) dy = 0$ (My answer: exact)

I am not sure if my answers are correct or if there are more options.

Thanks for any advice.

Last edited by skipjack; March 22nd, 2019 at 03:28 AM.
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March 22nd, 2019, 03:37 AM   #2
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(a) and (b) are first order, non-linear, homogeneous, non-separable ordinary differential equations.

Why did you think (c) is exact?
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