1. The solution of the following partial differential equation is

- sin(3x – y)
- 3x
^{2}+ y^{2} - sin(3x – 3y)
- (3y
^{2}– x^{2})

2. Consider the following partial differential equation

For this equation to be classified as parabolic, the value of B^{2} must be

- 1
- 2
- 3
- 4

3. Consider a function f(x,y,z) given by

f(x,y,z) = (x^{2} + y^{2} – 2z^{2})(y^{2} + z^{2})

The partial derivative of this function with respect to x at the point, x = 2, y = 1 and z = 3 is

- 50
- 40
- 30
- 10

4. Consider the following partial differential equation u(x,y) with the constant c > 1

Solution of this equation is

- u(x,y) = f(x + cy)
- u(x,y) = f(x – cy)
- u(x,y) = f(cx + y)
- u(x,y) = f(cx – y)

5. The type of partial equation

is

- elliptical
- parabolic
- hyperbolic
- none of these