dy/dx = (x + 3y)/(x - y)
A) Solve the Differential Eqn
B) Draw a Direction Field and some integral curves. Are they symmetric w/ respect to the origin?
I believe i solved the equation correctly, but i dont know how to draw the direction fields and integral curves. I tried plotting y v. y' in order to create the resulting direction field and integral curves, but i dont know what it looks like.
*Also, how do I integrate the left side? I just used an online calculator to get the answer, but i would like to know how to solve this
The Attempt at a Solution
A) After dividing by x and substituting v = y/x:
(1 + 3v)/(1 - v) = xv' + v
v' = (1/x)( (1 + 3v)/(1 - v) - v )
* (1-3v)/(1+3v) - 1/v dv = dx/x
After integrating and solving for c:
C = (2/3)ln(3y/x + 1) - y/x -ln(y/x) - ln(x)
Also, y = -x