Reposting the question in a more legible and understandable way again. The earlier one was flouting a few posting guidelines too.

So, I am trying to solve the heat conduction partial differential equation, I have two boundary conditions and this is how I have tried to model the DSolve/NDsolve arguments but have failed on both occasions.

Here is my code:

 pde = c*p*D[y[r, t], t] - k*D[y[r, t], {r, 2}] == q[r];       NDSolve[pde, y[r, 0] == 0, y[Infinity, t] == 0, y[r, t], {r, t}] 

This is what I get:

NDSolve::dsvar: y[\[Infinity],t]==0 cannot be used as a variable. 

I also used Dirichlet boundaries:

pde = c*p*D[y[r, t], t] - k*D[y[r, t], {r, 2}] == q[r]; NDSolve[pde, DirichletCondition[y[r, 0] == 0, True],  DirichletCondition[y[Infinity, t] == 0, t > 0], y[r, t], {r, t}] 

This is what I got this time:

NDSolve::litarg: To avoid possible ambiguity, the arguments of the  dependent variable in DirichletCondition[y[r,0]==0,True] should  literally match the independent variables. 

Getting the same error messages with both DSolve and NDSolve. Can’t really wrap my head around it. Where exactly am I going wrong?