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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

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# 2. order diff equation

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