Program Explanation Given information: The differential equation is d x d t = 3 x ( x − 5 ) and the initial condition is x ( 0 ) = 8 . Calculation: The given differential equation is d x d t = 3 x ( x − 5 ) . First separate the variables of the differential equation d x d t = 3 x ( x − 5 ) as, d x d t = 3 x ( x − 5 ) d x 3 x ( x − 5 ) = d t Use the partial fraction method to solve the given differential equation. Consider the coefficient of d x from above equation 1 3 x ( x − 5 ) 1 3 x ( x − 5 ) = a 3 x + b ( x − 5 ) .....(1) Now solve the above equation as, 1 3 x ( x − 5 ) = a 3 x + b ( x − 5 ) 1 x ( x − 5 ) = a ( x − 5 ) + 3 b x ( x ) ( x − 5 ) 1 = − 5 a + a x + 3 b x 1 = − 5 a + x ( a + 3 b ) Compare the coefficient of x and constant to obtain the value of a and b . a = − 1 5 , 3 b + a = 0 Therefore, the value of a and b is, a = − 1 5 , b = 1 15 Now substitute − 1 5 for a and 1 15 for b in equation (1). 1 3 x ( x − 5 ) = − 1 5 ( 3 x ) + 1 15 ( x − 5 ) Now integrate the differential equation on both sides. ∫ d x 3 x ( x − 5 ) = ∫ d t ∫ ( − 1 5 ( 3 x ) + 1 15 ( x − 5 ) ) d x = ∫ d t − 1 5 ln ( 3 x ) + 1 15 ln ( x − 5 ) = t + c 1 5 ln x − 5 x = 3 t + c Now simplify the further equation

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 2.1, Problem 8P

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

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Chapter 2.1, Problem 7P

Chapter 2.1, Problem 9P

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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 ( x − 5 ) 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(x−5) and then graph the solution.

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Chapter 2 Solutions