Differential EquationAnalytical solution for the differential equation that is enclosed in the black lines and how to arrive at the one that is enclosed in the red lines step by step. Temperature At time t = 0 minutes, the temperature of an object is 140°F. The temperatureof the object is changing at the rate given by the differential equation(y-72)dydt12(a) Use a graphing utility and Euler's Method to approximate the particular solutions of thisdifferential equation at t = 1, 2, and 3. Use a step size of h = 0.1. (A graphing utilityprogram for Euler's Method is available at LarsonCalculus.com.)(b) Compare your results with the exact solution y = 72 +68e-¹/2(c) Repeat parts (a) and (b) using a step size of h = 0.05 Compare the results

Answered: Image /qna-images/answer/1e716ce7-5c44-424c-a5e2-88d8fb56d944.jpg

Answered: Temperature At time t = 0 minutes, the…

Temperature At time t = 0 minutes, the temperature of an object is 140°F. The temperature of the object is changing at the rate given by the differential equation dy 1 dt 2 (y-72)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 22E

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Question

Differential Equation

Analytical solution for the differential equation that is enclosed in the black lines and how to arrive at the one that is enclosed in the red lines step by step.

Temperature At time t = 0 minutes, the temperature of an object is 140°F. The temperature
of the object is changing at the rate given by the differential equation
(y-72)
dy
dt
1
2
(a) Use a graphing utility and Euler's Method to approximate the particular solutions of this
differential equation at t = 1, 2, and 3. Use a step size of h = 0.1. (A graphing utility
program for Euler's Method is available at LarsonCalculus.com.)
(b) Compare your results with the exact solution y = 72 +68e-¹/2
(c) Repeat parts (a) and (b) using a step size of h = 0.05 Compare the results

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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