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General and particular solution for this first-order nonlinear ODE :


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And the stated problem is to prove something about the solution, or actually to write it down explicitly? – GEdgar Dec 15 '12 at 17:44



This belongs to an Abel equation of the second kind.

Let $x=e^{-t}$ ,

Then $\dfrac{dy}{dx}=\dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}}=\dfrac{\dfrac{dy}{dt}}{-e^{-t}}=-e^t\dfrac{dy}{dt}$



This belongs to an Abel equation of the second kind in the canonical form.

Please follow the method in

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