I am trying to solve a PDE in the first order with specific boundary conditions. When I solve use DSolve without the boundary conditions, Mathematica gives me an answer in an arbitrary function. When I put the boundary conditions, it doesn't solve it. Could someone please help me with this issue (word of caution: I am new to Mathematica). Thank you advance in time.
Code:
pde = D[S[x, y, z], x] + D[S[x, y, z], y] + D[S[x, y, z], z] - A*S[x, y, z] - B == 0
Here A and B are known constants and S[x,y,z] is the solution I am looking for.
Then I simply use
DSolve[{pde, S[0,y,z] ==0, S[x,y,0] ==0, S[x,0,z] ==0}, S[x,y,z] , {x,y,z}]
This returns me the output equivalent to the input! Thank you.