Understanding the Diffusion Equation for Water Pressure in Filtration Beds

[andrey21]

Water pressure in a filtration bed is given by the following diffusion equation:

$$\frac{\partial p}{\partial t} = -k$$

 

[andrey21]

Sorry I only published part of the question in the first post. Here it is in full:

Water pressure in a filtration bed is given by the following diffusion equation:

$$\frac{\partial P}{\partial t} = K \frac{\partial ²P}{\partial x²}$$

Where 0 < x < l t > 0

With Boundary conditions:

$$\frac{\partial P}{\partial x }\right|_x=0 = 0$$ P(l,t) = 100


Now the question is:

f(x) = ax + b

Find a and b such that
$$\frac{\partial f}{\partial x }\right|_x=0 = 0$$ and f(l) = 0

 

[snipez90]

Looks like standard separation of variables and use of Fourier series to me. What are you stuck on.