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I have a system of three coupled nonlinear ODEs:

[tex] \frac{d}{du}(nu)=exp(-\phi), [/tex]

[tex] u\frac{du}{dx}=\frac{d\phi}{dx}-\frac{u}{n}exp(-\phi), [/tex]

[tex] \frac{d^2 \phi}{dx^2}=n-exp(-\phi), [/tex]

with boundary conditions

[tex] \phi=\phi'=u=n=0 \text{ at } x=0 [/tex]

Does anyone know, or have references to, how to solve these with a series expansion? I am only interested in the solution for [tex]x \ll 1 [/tex], so higher order terms can be neglected.

Thankful for any help!

/Daniel

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# Series solution to coupled nonlinear ODEs

Can you offer guidance or do you also need help?

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