anonymous
  • anonymous
(3x-y-6)dx+(6x-2y-6)dy=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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dumbcow
  • dumbcow
this is not an exact equation...seems the solution cant be found using elementary functions http://www.wolframalpha.com/input/?i=%283x-y-6%29dx%2B%286x-2y-6%29dy%3D0 to get started you need to reduce it down to 1-variable equation notice both terms have a factor of "3x-y" let u = 3x-y --> du/dx = 3- dy/dx \[(u-6) + (2u-6)(3-\frac{du}{dx}) = 0\] now you can try to solve for u(x) by separating variables \[\frac{du}{dx} = \frac{7u-24}{2u-6}\] \[\int\limits \frac{2u-6}{7u-24} du = \int\limits dx\] \[\frac{2}{49}(7u-24)+\frac{6}{49}\ln (7u-24) = x +C\] now you get stuck because there is no way to algebraically isolate "u" if you could then final solution would be \[y = 3x -u(x)\]

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