Consider the Differential Equation $x \frac { d y } { d x } - 3 y = 0$

question 9

Essay

Consider the differential equation $x \frac { d y } { d x } - 3 y = 0$ .(a) Sketch the direction field. Indicate where the slopes are $- 1$ , 0, or 1. Draw some other slopes as well.(b) If the point $( 1,2 )$ is on the graph of a solution, use Euler's Method with step size $0.5$ to estimate the value of the solution at $x = 2$ .

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Definitions:

Organogenesis

The process by which the organs and tissues develop from the embryonic cells during development.

Embryonic Development

The process by which an embryo forms and develops, involving cell division, cell differentiation, and morphogenesis.

Invagination

A process in developmental biology where a part of the cell or tissue surface folds inward to form a pocket or pouch.

Organogenesis

The phase of embryonic development concerned with the formation of organs and organ systems.