This question is related to a mechanics problem for which I have already done the dynamics side of it and have now reduced it down to this but I'm having trouble evaluating this differential equation.

$$\frac{ds}{dt}=\sqrt{(2g\sin\alpha) s}$$

I can see that I need to separate variables but I'm not sure how to proceed from here.

Any help would be appreciated.

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    $\begingroup$ Is $\alpha$ function of $t$ or of $s$ ? If not the ODE is separable : use the straightforwardl integration method. $\endgroup$ – JJacquelin Mar 10 '16 at 16:48
  • $\begingroup$ $\alpha$ was just the angle that the plane was inclined at, so no it isn't a function of $t$ or $s$. $\endgroup$ – MHW Mar 10 '16 at 16:53

$$\frac{ds}{dt}=\sqrt{(2g\sin\alpha) s}$$


$$\int\frac{ds}{\sqrt{s}}=\sqrt{2g\sin\alpha}\int dt$$ $$2\sqrt{s}=\sqrt{2g\sin\alpha}\:t+\text{constant}$$

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