Eliminate the arbitrary function f and g from z = f(x+iy) + g(x-iy) and form a partial differential equation.

Form partial differential equation by eliminating arbitrary function 

z =  x + y + f(xy)

Eliminating arbitrary constants form partial differential equation from the 

z = ax + by

Solve the following partial differential equation 

(1).         pq + p + q = 0

(2).         pq = 1

Prove Green's theorem in a plane.

Using double integral find the area enclosed by the curve y= 2x² and y²=4x

Find the area bounded by the parabola y²= 4 - x and y² = 4 - 4x as a double integral and evaluate it.

Using double integration find the area of parallelogram whose vertices are A(1,0), B(3,1), C(2,2), D(0,1) .

Evaluate the area bounded by y = x and y = x²

Evaluate the area bounded by               y = 4x - x² and y = x

Find the area bounded by y² = 4 - x ,    y² = x