Program Explanation Given information: The differential equation is d x d t = 3 x ( 5 − x ) and the initial condition is x ( 0 ) = 8 . Calculation: The given differential equation is d x d t = 3 x ( 5 − x ) . First separate the variables of the differential equation d x d t = 3 x ( 5 − x ) as, d x d t = 3 x ( 5 − x ) d x x ( 5 − x ) = 3 d t Use the partial fraction method to solve the given differential equation. Consider the coefficient of d x from above equation 1 x ( 5 − x ) 1 x ( 5 − x ) = a x + b ( 5 − x ) .....(1) Now solve the above equation as, 1 x ( 5 − x ) = a x + b ( 5 − x ) 1 x ( 5 − x ) = a ( 5 − x ) + b x ( x ) ( 5 − x ) 1 = 5 a − a x + b x 1 = 5 a + x ( − a + b ) Compare the coefficient of x and constant to obtain the value of a and b . a = 1 5 , b − a = 0 Therefore, the value of a and b is, a = 1 5 , b = 1 5 Now substitute 1 5 for a and 1 5 for b in equation (1). 1 x ( 5 − x ) = 1 5 x + 1 5 ( 5 − x ) Now integrate the differential equation on both sides. ∫ d x x ( 5 − x ) = ∫ 3 d t ∫ ( 1 5 x + 1 5 ( 5 − x ) ) d x = ∫ 3 d t 1 5 ln ( x ) − 1 5 ln ( 5 − x ) = 3 t + c 1 5 ln x 5 − x = 3 t + c Now simplify the further equation

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ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 2.1, Problem 5P

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Program Description: Purpose of the problem is to find the particular solution of the differential equation dxdt=3x(5−x) and then graph the solution.

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Chapter 2.1, Problem 4P

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Program Description: Purpose of the problem is to find the particular solution of the differential equation d x d t = 3 x ( 5 − x ) and then graph the solution.

Solution Summary: The author explains that the problem is to find the particular solution of the differential equation and graph the solution.

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Program Description: Purpose of the problem is to find the particular solution of the differential equation dxdt=3x(5−x) and then graph the solution.

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Chapter 2 Solutions