# How to find the particular solution of the differential equation using method of initial parameters

$$$$\frac{\text d^4w}{\text dy^4}-2\,(n\pi)^2\,\frac{\text d^2w}{\text dy^2}+\Big((n\pi)^4- \alpha^4\Big)\,w=C_{n}\,\delta(y-\zeta)\\$$$$

I am trying to find the particular integral of the above-mentioned differential equation. The objective is to find the green function by using this method. In one of the reference (cf. [1], from Eq. (14)) they explained first by extracting the homogenous solution $w$ and after that assuming some constants for the homogeneous solution $w$, and its 1st,2nd,3rd derivatives when evaluated at $y=0$, Now we have four equations for unknowns and solve for unknown coefficients. But it is not quite clear. This derivation starts from Eq. (14) in [1], I understand till Eq. (38), after that i am pretty much lost.

[1] L.A. Bergman, J.K. Hall, G.G.G. Lueschen, D.M. McFarland: "Dynamic Green's functions for Levy plates", J. Sound Vib. 162-2 (1993), 281-310. doi:10.1006/jsvi.1993.1119

• i have no idea what you are talking about, but Fouriertransform should do a pretty good job in solving this DE Feb 24, 2018 at 11:19
• Just want to extract the particular integral part of the differential equation using method of initial parameters Feb 24, 2018 at 15:31
• @YuriyS Thanks. Feb 24, 2018 at 17:19
• What is that reference you mention? Could you give a link? Feb 24, 2018 at 23:28
• Feb 25, 2018 at 4:49