- #1
Jeppe
- 2
- 0
Hi all!
I am trying to solve the following differential equation for the electron distribution in a SOI MOSFET structure.
The equation is:
[tex]\frac{d^2n}{dx^2} = \frac{1}{n}\left( \frac{dn}{dx}\right)^2 + A n^{2} [/tex]
A is a constant.
The boundary conditions are:
n(0) = c1 (a constant)
n'(0) = 0
I know that the solution to the equation is:
[tex]n(x) = \frac{c1}{cos^2\left( \sqrt{\frac{1}{2} A \,c1}\,\,\, x \right)}[/tex]
but i can not solve it myself. I have tried with both maple, mathematica, and MATLAB but none of them seems to be able to solve it.
Could anyone give me a hint on how to do it?
Thanks!
Jeppe
I am trying to solve the following differential equation for the electron distribution in a SOI MOSFET structure.
The equation is:
[tex]\frac{d^2n}{dx^2} = \frac{1}{n}\left( \frac{dn}{dx}\right)^2 + A n^{2} [/tex]
A is a constant.
The boundary conditions are:
n(0) = c1 (a constant)
n'(0) = 0
I know that the solution to the equation is:
[tex]n(x) = \frac{c1}{cos^2\left( \sqrt{\frac{1}{2} A \,c1}\,\,\, x \right)}[/tex]
but i can not solve it myself. I have tried with both maple, mathematica, and MATLAB but none of them seems to be able to solve it.
Could anyone give me a hint on how to do it?
Thanks!
Jeppe