Thank you for your comment, I will try to better specify the problem that I am dealing with: I am seeking a solution for the biharmonic equation (1) f,xxxx+2*f,xxyy+f,yyyy=0 that governs problems in plane elasticity. I am seeking for solutions in the form (2) g(x,y)=exp(-k*x)*F(y) where k is a constant that may be complex. Substituting into (1) f(x,y) by g(x,y) yields the following fourth order equation F,yyyy+2*k^2*F,yy+k^4*F=0 The domain for F is [-h/2,h/2] Assuming for boundary conditions F(h/2)=0 F(-h/2)=0 F,y(h/2)=0 F,y(-h/2)=0 Which correspond admitting a traction free condition on the edge of a membrane [0,L]x[-h/2,h/2] An eigenvalue problem associated with the differential equation is obtained and the corresponding complex eigenvalues are the nonzero roots of the transcendental equations sin(2*k)-2*k=0 sin(2*k)+2*k=0