(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

Chapter 2 Solutions

Advanced Engineering Mathematics

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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.

Concept explainers

Videos

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