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# Solving a mathematical problem

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#### engtokhy

##### Newbie level 6
Please i want to solve the following eqution by maple 4 or any package or how i can solve it

δΦ²/δx²+δΦ²/δy²+Φ/τ-Φ×(S-G)=0

Where τ, S, and G are constants
at the boundary condition

δΦ/δx =0 at x=Lx
δΦ/δy =0 at y=Ly

Lx and Ly are the lengths which the electron will move inside the quantum well
please try to help me as possible {the domain of the problem is x-y}

Many thanks

Is this a strict requirement that it needs to be solved by a "package"? Can we solve it by hand? (just joking )

The problem as you specified it is not well defined. Since this is a 2D problem, you need to specify the boundary condition at the boundary of your 2D domain. What is the domain? (i.e. x-y region where you need to solve your equation).

What's L and K?

Can you group "Φ/τ-Φ×(S-G)" into "a*Φ", where a=1/τ-(S-G) ?

I have an idea but i dont know it's usefull for you:
Φ=XY;
Φ/τ-Φ×(S-G)=aΦ;
then: YX"+XY'=aXY;
X"/X+Y"/Y=a;
X"/X=m1;Y"/Y=m2;that m1+m2=a;
you can discuss about m1,m2,and boundary condition.

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