Differential Equation problem: 2 Dec'15


A sherical raindrop evaporate at a rate proportional to its surface area at any instant t.
The differential equation giving the rate of change of radius of raindrop has degree?

!!a)" "1!!

!!b)" "2!!

!!c)" "!!Can be both

!!d)" "!!None


For a sherical raindrop, the rate of evaporation is proportional to its surface area.

Hence, !!(dV)/dt prop surface area!!

!!(dV)/dt = lambda4pir^2!!........(i)

Volume of sphere = !!(4/3)pir^3!!

Putting this in equation (i), we get

!!(d(4/3 pir^3))/dt = lambda4pir^2!!

!!=> (3r^2)/3(dr)/dt = lambdar^2!!

!!=> (dr)/dt = lambda!!

So !!degree = 1!!