Partial Differential Equations MCQ

1. The solution of the following partial differential equation is

1. sin(3x – y)
2. 3x2 + y2
3. sin(3x – 3y)
4. (3y2 – x2)

2. Consider the following partial differential equation

For this equation to be classified as parabolic, the value of B2 must be

1. 1
2. 2
3. 3
4. 4

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

f(x,y,z) = (x2 + y2 – 2z2)(y2 + z2)

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

1. 50
2. 40
3. 30
4. 10

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

Solution of this equation is

1. u(x,y) = f(x + cy)
2. u(x,y) = f(x – cy)
3. u(x,y) = f(cx + y)
4. u(x,y) = f(cx – y)

5. The type of partial equation

is

1. elliptical
2. parabolic
3. hyperbolic
4. none of these
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