Use the fourth-order Runge-Kutta subroutine with h = 0.4 to approximate the solution to the following initial value problem at x = 0, 0.4, 0.8, ..., 12. Use your answers to
make a rough sketch of the solution on [0,12]. Note whether or not $\frac{\partial f}{\partial y}$ is bounded.
y'= cos (8y) + 2x, y(0) = 3
Let y' = f(x,y). Find $\frac{\partial f}{\partial y}$ and determine whether or not it is bounded on the vertical strip S = {(x,y): 0<x<12, $-\infty$ <y<$\infty$}. Select the correct choice below and fill in the
answer box to complete your choice.
A. $\frac{\partial f}{\partial y}$(x,y) = is bounded.
B. $\frac{\partial f}{\partial y}$(x,y) = is not bounded.