anonymous
  • anonymous
solve the following equation if it is exact: (dy/dx)=(2xy-3x^2-2)/ (6y^2-x^3+3)
Mathematics
schrodinger
  • schrodinger
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schrodinger
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anonymous
  • anonymous
find the antiderivative?
anonymous
  • anonymous
I don't think this is exact, since if you arrange it in the appropriate form,\[(6y^2-x^3+3)dy=(2xy-3x^2-2)dx\]\[=(3x^2-2xy+2)dx+(6y^2-x^3+3)dy=0\]is exact if and only if\[\frac{\partial (3x^2-2xy+2)}{\partial y}=\frac{\partial (6y^2-x^3+3)}{\partial x}\]
anonymous
  • anonymous
it is a differential equation and I think it can be turned into a ratio-dependent differential equation and then into a separable differential equation however I don't know how to put it in a ratio dependent form

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anonymous
  • anonymous
\[LHS = -2x \neq -3x^2 = RHS\]

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