Assignment:
Q1) Find a vector normal to the surface z + 2xy = x2 + y2 at the point (1,1,0).
Q2) Determine if there are separable differential equations among the following ones and explain:
a) dy/dx=sin(xy),
b) dy/dx = (xy)/(X+y)
c) dr/d(theta) = (r^2+1)cos(theta)
Q3) Find the general solution of the differential equation
dy/dx = (3x^2)/ (y - sin y)
Provide complete and step by step solution for the question and show calculations and use formulas.