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

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 $x = 2$ .