Show that dx/dt = ln(1+2x+2y), dy/dt = x/2 - y - x^2/2 has an unstable critical point at (0,0). I could draw the direction field, but how do you show this analytically? Can you get a closed form solution of this system? It reduces to:
dy/dx = [ x/2 - y - x^2/2 ] / [ ln(1+2x+2y) ]
Thanks in advance.