Question

y'+(1/t)y=3cos2t
draw a direction field and find the general solution for the differential equation

Answer 1

I know how to solve the problem, I mainly need someone to explain how to draw a direction field?

Answer 2

I was typing solution this whole time and didn't realize you typed that, lol. To draw direction field, solve for y' and you get 3cos(2t) - (1/t)y. Now take a graph where the horizontal axis is the t-axis and the vertical axis is the y-axis. Take several points and plug in the value of t and y in the equation to find the slope at that point. So then draw a small line indicating the slope at each point. For example, the point (0, 0) has a slope 3 so you draw a little line that indicates a high positive slope. Keep doing that until the overall layout of the direction field is clear.

Answer 3

I can't tell f I was way too elaborate or just stating the obvious, lol.

Answer 4

familiar wid isoclines ?

Answer 5

thank you bagajr that was very helpful!