MATLAB: How to find eigenvalues for a system of lenearized ordinary differential equations

eigenvalue problemode's

I have a system of linearized ODEs with corresponding boundary conditions.
%—————————-system of ODEs————————————–%
y'(1)=y(2)
y'(2)=y(3)
y'(3)=(phi./Da).*y(2)+(2.*phi.*Fr./A1).*fd.*y(2)-(fd1.*1./A1).*y(3)-(fdd.*1./A1).*y(1)+(2.*fd.*1./A1).*y(2)-(e./A1).*y(2)-(phi.*Ra./(A1^2).*A2).*y(4)
y'(4)=y(5)
y'(5)=-(Pr./A2).*(fd.*y(5)+thd.*y(1)+e.*y(4))];
%—————————boundary conditions———————————-%
y(1)=y(2)=y(4)=0 at eta=0
y(2)=y(4)=0 at eta=0;
here Pr phi Ra Da Fr A1 A2 fd1 fd fdd thd are known quantities and 'e' is unknown.
I need to solve the system to find out the eigenvalues (e).
Thanks in advance.

Best Answer

Tanya, hi.
write so:
dyi/dt =...y1 (t)+...y2 (t)+...+y5(t);
let x (t)=[y1;y2;...;y5]; ->
((V/ve) x=Ah; A - matrix coeff. Your system. Let's formally denote d/dt=p
px-Ax=0; - > (p*E-A) x=0; since x is not 0, then
det(p*E-A)=0. This is the equation for the eigenvalues of p.
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