Explanation Approach: Use the variable separable method to obtain the solution. Calculation: Consider the differential equation. d v d t = 1 2 ( 25 − v ) , t > 0 …… ( 1 ) Using variable separable method, d v 25 − v = 1 2 d t …... ( 2 ) Integrate both sides the equation ( 2 ) . ∫ d v 25 − v = ∫ 1 2 d t To determine (b) To sketch: The slope field for the differential equation d v d t = 1 2 ( 25 − v ) , t > 0

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ISBN: 8220102019799

Author: ANNIN

Publisher: YUZU

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Question

Chapter 1.12, Problem 13AP

To determine

(a)

To verify:

Whether the solution of the differential equation dvdt=12(25−v), t>0 is v(t)=25.

To determine

(b)

To sketch:

The slope field for the differential equation dvdt=12(25−v), t>0

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Chapter 1.12, Problem 12AP

Chapter 1.12, Problem 15AP

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS AND LINEAR A

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(a) To verify: Whether the solution of the differential equation d v d t = 1 2 ( 25 − v ) , t &gt; 0 is v ( t ) = 25 .

(a) To verify: Whether the solution of the differential equation dvdt=12(25−v), t>0 is v(t)=25.

(b) To sketch: The slope field for the differential equation dvdt=12(25−v), t>0

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Chapter 1 Solutions

(a) To verify: Whether the solution of the differential equation d v d t = 1 2 ( 25 − v ) , t > 0 is v ( t ) = 25 .

(a)

To verify:

Whether the solution of the differential equation dvdt=12(25−v), t>0 is v(t)=25.

(b)

To sketch:

The slope field for the differential equation dvdt=12(25−v), t>0