I am trying to find a Green's function for a third order ODE.(adsbygoogle = window.adsbygoogle || []).push({});

([itex]\lambda[/itex] - d^{3}/dx^{3}- [itex]\mu[/itex] d/dx)u = f(x) with boundary conditions u(0) = u_{xx}(0) = u_{x}(L) = 0 (L is finite).

This has solution u(x) = c_{1}e^{m1x}+ c_{2}e^{m2x}+ c_{3}e^{m3x}

where m_{1}, m_{2}and m_{3}are the roots of the characteristic equation from the ODE (they are not important at the moment).

My question is how do I find the coefficients c_{1}, c_{2}and c_{3}?

I know that it is going to be a 3 term piecewise function (as it is third order).

Do I use the u(0) = u_{xx}(0) = 0 BC's from 0 to s and u(0) = u_{x}(L) = 0 from s to L?

I need help on this please.

Cheers.

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# Green's function for third order ODE

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