Chapter 8 - Mathematical Modeling With Differential Equations - 8.1 Modeling With Differential Equations - Exercises Set 8.1 - Page 567: 21

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

$y' = 2 - 4x$ to find $y$, integrate $y'$ $ y = \int (2 - 4x) dx$ $y = - 2x^2 + 2x + C$ Find C when $y(0) = 3 $ $3 = - 2(0)^2 + 2(0) + C$ $ C = 3 $ Rewrite the equation with the value of C $y = - 2x^2 + 2x + 3$