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I have a fourth order non homogenous differential equation of the form

$$ay^{(4)}+by''+cy=d$$

This actually came from a coupled system of second order non homogenous differential equations, if that is easier to solve:

$$y''=ax+by+c$$ $$x''=dx+fy+g$$

I believe I know how to solve the homogenous form of the fourth order equation, but I don't know how to solve it with the addition of the constant term. Any help would be appreciated!

Edit: This problem arose from an analysis of a double spring system using Lagrangian mechanics. You can see an example of the system here.

Thanks

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    Are $a,b,c,d$ constants? – 2017-01-10
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    Yeah, all letters are constants (other than x and y) – 2017-01-10
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    Use the method of undetermined coefficients (there are countless references to this) to find a particular solution (of the nonhomogeneous equation). Then the solution to the homogeneous equation can be added to the particular solution to give a general solution to the nonhomogeneous equation. – 2017-01-10

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