(a) Explanation Given: The differential equation is d v d t + 3 ( k ρ ) ( k ρ ) t + r 0 v = g . Procedure used: 1. Write the DE equation. 2. Find the integrating factor. 3. Obtain the final solution of differential equation. 4. Substitute the condition for obtaining the constant value. Calculation: The differential equation is given by, d v d t + 3 ( k ρ ) ( k ρ ) t + r 0 v = g Here, let k ρ = b , d v d t + 3 b b t + r 0 v = g (1) The solution of differential equation is, v ( I .F ) = ∫ g ( I .F ) d t + c (2) Obtain integrating factor of differential equation in equation (1). I .F = e ∫ 3 b b t + r 0 d t I .F = e 3 ln | b t + r 0 | I .F = ( b t + r 0 ) 3 Substitute ( b t + r 0 ) 3 for I .F in equation (2) and integrate. v ( b t + r 0 ) 3 = ∫ g ( b t + r 0 ) 3 d t + c v ( b t + r 0 ) 3 = g 4 b ( b t + r 0 ) 4 + c (3) Substitute 0 for t and 0 for v in equation (3) (b) To determine To show: The radius of the raindrop at time t is r ( t ) = ( k ρ ) t + r 0 . To determine (c) Find the time at which the raindrop has evaporated completely.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

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Chapter 2.7, Problem 39E

(a)

To determine

The solution of the differential equation for v(t) if the raindrop falls from the rest.

(b)

To determine

To show: The radius of the raindrop at time t is r(t)=(kρ)t+r0.

To determine

(c)

Find the time at which the raindrop has evaporated completely.

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Chapter 2.7, Problem 38E

Chapter 2.7, Problem 40E

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The solution of the differential equation for v ( t ) if the raindrop falls from the rest.

Solution Summary: The author explains the differential equation for v(t) if the raindrop falls from the rest.

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The solution of the differential equation for v(t) if the raindrop falls from the rest.

To show: The radius of the raindrop at time t is r(t)=(kρ)t+r0.

(c)

Find the time at which the raindrop has evaporated completely.

Want to see the full answer?

Chapter 2 Solutions