Page:Calculus Made Easy.pdf/257

 curve y becomes either a maximum or a minimum, so that $$\dfrac{dy}{dx} = 0$$, then $$y$$ will have the value $$= \dfrac{g}{a}$$. But let us go to work as before, separating the differentials and trying to transform the thing into some integrable shape.

Now we have done our best to get nothing but $$y$$ and $$dy$$ on one side, and nothing but $$dx$$ on the other. But is the result on the left side integrable?

It is of the same form as the result on p. 148; so, writing the instructions to integrate, we have:

and, doing the integration, and adding the appropriate constant,

which is the solution.