# How to write code for solving a second order differential equation? [closed]

I am new to Mathematica and am trying to figure out how to solve the following second order partial differential equation using DSolve.

$\qquad U C_{x}+V C_y= C_{xx}+ C_{yy}+ C_{zz} + q' \delta(x)\,\delta(y)\,\delta(z)$

where $U=uK_x^{-1/2},\ V=vK_y^{-1/2},\ q'=q(k_x k_y k_z )^{-1/2}$ with two boundary conditions given by

1. $\qquad C\rightarrow 0$ as $|x|,|y|,z\rightarrow \infty$

2. $\qquad -K_zC_z=0$ at $z=0$

So far I have written code as

pde =
u Sqrt[kx] D[c[x, y, z], x] + v Sqrt[ky] D[c[x, y, z], y]  ==
D[c[x, y, z], {x, 2}] + D[c[x, y, z], {y, 2}] + D[c[x, y, z], {z, 2}] +
q Sqrt[kx ky kz] DiracDelta[x] DiracDelta[y] DiracDelta[z]


but I don't know how to write the boundary conditions.

Also,

DSolve[pde, c[x, y, z], {x, y, z}]


returns

$\qquad \mathsf{DSolve}\left[\sqrt{\text{kx}}\,u\,c^{(1,0,0)}(x,y,z) + \sqrt{\text{ky}}\,v\,c^{(0,1,0)}(x,y,z) = c^{(0,0,2)}(x,y,z) + c^{(0,2,0)}(x,y,z)+c^{(2,0,0)}(x,y,z) + q\,\delta(x)\,\delta(y)\,\delta(z) \sqrt{\text{kx}\,\text{ky}\,\text{kz}}\,c(x,y,z),\{x,y,z\}\right]$

but does not solve the problem.

• Katherina, DSolve  cannot do that. You need to go for NDSolve , that is, to solve it numerically, then see Menu/Help/WolframDocumentation/NDSolve/Scope/PartialDifferentialEquations. Another way is to go to the k-space and solve it it analytically. This latter way I recommend. Have fun! – Alexei Boulbitch Sep 24 '15 at 8:46