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I've encountered this equation: $$S(t)-y(t)=\alpha \left(\frac{dy(t)}{dt}\right)^2$$ where $S(t)$ is a non-defined source (input of our system) and $\alpha$ is a positive constant. I've tried variable separation but without any success. Please, can someone help me find a solution or a possible approach?

Thanks

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  • $\begingroup$ This is equation: $\alpha(y’)^2=S-y$? $\endgroup$ – player100 Nov 29 '18 at 17:29
  • $\begingroup$ Yes! I think that take the derivative of both sides by the variable $t$ produces something similar to the Abel differential equation... But I don't know how to proceed $\endgroup$ – Luca Savant Nov 30 '18 at 22:16
  • $\begingroup$ I think that an Abel form is the best you can hope for. Without knowing more about the structure of $S$, it is hard to proceed in generality. $\endgroup$ – player100 Dec 2 '18 at 3:30

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