A differential equation is d 2 y d t 2 = A y 2 + B y t where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous. | bartleby

International Edition---engineerin...

4th Edition

Andrew Pytel And Jaan Kiusalaas

Publisher: CENGAGE L

ISBN: 9781305501607

Chapter 1, Problem 1.10P

Textbook Problem

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A differential equation is d 2 y d t 2 = A y 2 + B y t where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous.

To determine

The dimensions of constants A and B.

Explanation of Solution

The equation,

d2ydt2=Ay2+Byt, is dimensionally homogeneous.

[y]=[L][t]=[T]

Calculation:

The given equation is dimensionally homogeneous.

d2ydt2=Ay2+Byt[ d 2yd t 2]=[Ay2]=[Byt]

Take the first part of equation,

[ d 2yd t 2]=

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International Edition---engineering Mechanics: Statics, 4th Edition

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