Program Explanation Given information: The differential equation is d x d t = 9 − 4 x 2 and the initial condition is x ( 0 ) = 0 . Calculation: The given differential equation is d x d t = 9 − 4 x 2 . First separate the variables of the differential equation d x d t = 9 − 4 x 2 as, d x d t = 9 − 4 x 2 d x 9 − 4 x 2 = d t d x ( 3 + 2 x ) ( 3 − 2 x ) = d t Use the partial fraction method to solve the given differential equation. Consider the coefficient of d x from above equation 1 ( 3 + 2 x ) ( 3 − 2 x ) 1 ( 3 + 2 x ) ( 3 − 2 x ) = a 3 + 2 x + b ( 3 − 2 x ) .....(1) Now solve the above equation as, 1 ( 3 + 2 x ) ( 3 − 2 x ) = a 3 + 2 x + b ( 3 − 2 x ) 1 ( 3 + 2 x ) ( 3 − 2 x ) = a ( 3 − 2 x ) + b ( 3 + 2 x ) ( 3 + 2 x ) ( 3 − 2 x ) 1 = 3 a − 2 a x + 3 b + 2 b x 1 = 3 a + 3 b + x ( − 2 a + 2 b ) Compare the coefficient of x and constant to obtain the value of a and b . 3 a + 3 b = 1 , b − a = 0 Therefore, the value of a and b is, a = 1 6 , b = 1 6 Now substitute 1 6 for a and 1 6 for b in equation (1). 1 ( 3 + 2 x ) ( 3 − 2 x ) = 1 6 ( 3 + 2 x ) + 1 6 ( 3 − 2 x ) Now integrate the differential equation on both sides. ∫ d x ( 3 + 2 x ) ( 3 − 2 x ) = ∫ d t ∫ ( 1 6 ( 3 + 2 x ) + 1 6 ( 3 − 2 x ) ) d x = ∫ d t 1 12 ln ( 3 + 2 x ) − 1 12 ln ( 3 − 2 x ) = t + c 1 12 ln 3 + 2 x 3 − 2 x = t + c Now simplify the further equation

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ISBN: 9780100802452

Author: Calvis

Publisher: YUZU

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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 dxdt=9−4x2 and then graph the solution.

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Chapter 2.1, Problem 3P

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 d x d t = 9 − 4 x 2 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=9−4x2 and then graph the solution.

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Chapter 2 Solutions