My Math Forum Help classifying DEs

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 March 21st, 2019, 04:26 AM #1 Newbie   Joined: Jul 2018 From: Australia Posts: 2 Thanks: 0 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.
 March 22nd, 2019, 03:37 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,921 Thanks: 2203 (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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