A hemispherical bowl has a radious of R (metres) and at a time t = 0 is full of water. At that moment a circular hole of radius a (centimetres) is opened in the bottom of the bowl. Let y be the vertical height of the water above the hole at time t. Then y is governed by the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\pi(Ry-y^2)\frac{dy}{dt} = -\pi(a10^{-2})^2\sqrt{2gy},[/tex]

where [tex]g = 9.8m/s^2[/tex] is gravity.

Solve this differential equation to find y as an implicit function of t.

I need help with this. Im unsure of how to start. Do i try gather all the y terms on one side and everything else on the other?

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# Homework Help: Differential Equation of a hemispherical bowl

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