Use Euler's Method with Five Steps to Approximate a Solution $$y^{\prime}=\cos y$$

question 120

Essay

Use Euler's method with five steps to approximate a solution to the differential equation $$y^{\prime}=\cos y$$
given that
$$y(0)=-1$$
. Give both a numerical solution by filling in the table of values, and a graphical solution by plotting your points.
$\begin{array}{ll}x & y \\0 & -1 \\0.3 & \\0.6 & \\0.9 & \\1.2 & \\1.5 &\end{array}$

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Definitions:

Anterior Fontanel

The soft spot on a baby's skull where bone formation is not yet complete.

Occipital Bone

A cranial bone located at the back and base of the skull, crucial for head movement and support.

Sagittal Suture

A fibrous joint that connects the two parietal bones of the skull, running from the front to the back of the head.

Sternocostal Synchrondrosis

A type of joint where the first rib meets the sternum, characterized by its cartilaginous connection that allows for some movement.