Chapter 3.7, Problem 15E

To determine

To approximate:

The solution to the initial value problem $y^{\prime }=\cos \left(5y\right)-x$ at $x=0,0.1,0.2,\mathrm{...},3.0$ and to make a rough sketch of the solution on $\left[0,3\right]$.

Solution:

The approximate solution for the initial value problem $y^{\prime }=\cos \left(5y\right)-x$ is shown in Table (1), and the graph plotted for those solutions are shown in Figure (1).