1 (i).

The partial differential equation is the one-dimensional heat conduction equation:

and the subsidiary conditions are:

(ii)

The partial differential equation is the one-dimensional wave equation:

and the subsidiary conditions are (note that there are no initial conditions given here, so that it would be impossible to obtain a complete solution of the partial differential equation):

(Remember the notation )

2. (i)

(ii)

(iii)

(iv)

3(i)

(ii)

(iii)

4.(i)

Ordinary Differential Equation

Partial Differential Equation

(ii)

Ordinary Differential Equation

Partial Differential Equation