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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, nonlinear, homogeneous, nonseparable ordinary differential equations. Why did you think (c) is exact? 

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