`g'(x) = 4x^2, g(-1) = 3` Find the particular solution that satisfies the differential equation.

Textbook Question

Chapter 4, 4.1 - Problem 36 - Calculus of a Single Variable (10th Edition, Ron Larson).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use direct integration to evaluate the general solution to the differential equation:

`int (4x^2)dx = 4x^3/3 + c`

You need to find the particular solution using the information provided by the problem, that g(-1) = 3, such that:

`g(-1) = (4/3)*(-1)^3 + c => 3 = -4/3 + c => c = 3 + 4/3 => c = 13/3`

Hence, evaluating the particular solution to the given differential equation yields `g(x) = 4x^3/3 + 13/3.`

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