1) Find a vector normal to the surface z + 2xy = x2 + y2 at the point (1,1,0).
2) Determine if there are separable differential equations among the following ones and explain:
b) dy/dx = (xy)/(X+y)
c) dr/d(theta) = (r^2+1)cos(theta)
3) Find the general solution of the differential equation
dy/dx = (3x^2)/ (y - sin y)
This solution tells what is a separable differential equation and explains how to solve a separable differential equation.