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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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Chapter
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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Writing and Solving a Differential Equation In

Exercises 13 and 14, write and find the general solution of the differential equation that models the verbal statement

The rate of change of Q with respect to t is inversely proportional to the square of t.

To determine

To calculate: The general solution for the differential equation which models the given verbal statement, ‘the rate of change of Q is inversely proportional to the square of t with respect to t’.

Explanation

Given:

The rate of change of Q is inversely proportional to the square of t with respect to t.

Formula used:

Integration of xn:

xndx=xn+1n+1+C

Calculation:

If the rate of change of Q is inversely proportional to t with respect to t, then the differential equation is given by:

dQdt 1t2

By using the proportionality constant k in above equation:

dQdt =k1t2

Multiplying the above equation by dt on both sides, we get:

dQdt

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