Chapter 8 - Mathematical Modeling With Differential Equations - 8.1 Modeling With Differential Equations - Exercises Set 8.1 - Page 567: 22

$y = -x^3 +2x +1$

$y'' = -6x$ $y' =\int(-6x) dx = -3x^2 + C. $ Find C when $y'(0) = 2 $ $2 = -3(0)^2 + C$ $c = 2$ Rewrite the equation $y'$ $y' = -3x^2 + 2$ Now find y $y = \int (-3x^2 + 2) = $ $ y = -x^3 +2x +D$ Find C when $y(0) = 1 $ $1 = -(0)^3 +2(0) +D$ $D = 1$ Rewrite equation $y$ $y = -x^3 +2x +1$