Chapter 8 - Mathematical Modeling With Differential Equations - 8.1 Modeling With Differential Equations - Exercises Set 8.1 - Page 567: 19

$c_1 =1$ $c_2 = 1$ $y = sin 2x +cos 2x$

$y = c_1 sin 2x + c_2 cos 2x$ $y' = 2c_1 cos 2x - 2c_2 sin 2x$ Plug in the value $y(0) = 1$ $y(0) = c_1 sin 2(0) + c_2 cos 2(0) = 1$ $c_2 = 1$ Plug in the value $y'(0) = 2$ $y'(0) = 2c_1 cos 2(0) - 2c_2 sin 2(0)= 2$ $2c_1 = 2$ $c_1 = 1$ we get $c_1 =1$ $c_2 = 1$ Rewrite the original equation with values of $c_1$ and $c_2$ $y = sin 2x +cos 2x$