# A bit about differential equations

1. Sep 12, 2009

### Luongo

For first order linear differential equations when is it alright to use the
dy/y-b/a = -adt form and when you must use the integration factor technique? In general i was able to obtain a solution using both methods.

Also, how do i draw a direction field which contains both t and y variables without solving and graphing the differential equation? i can only obtain the direction field at y = 0, it becomes too complicated if t is not 0, does anyone have any tips for drawing direction fields where y,t are variables for y'?

2. Sep 13, 2009

### HallsofIvy

Staff Emeritus
You use whatever method is easiest. There always exist an integrating factor but, except for linear equations, it may be very difficult to find. As for "dy/y- b/a= -adt", I don't know what you mean. It is impossible to have a differential equation of that form. If any term of a differential equation has the differentials, dy and dt, every term must.

If you are given dy/dt= f(t,y) then drawing the direction field at (t,y) is just a matter of evaluating f(t,y). Why should that be any easier at y= 0?