Solving 2nd order inhomogeneous equation

[Behroz]

Let's say that I solve a inhomogeneous differential equation of
the type d2y/dx2+k*dy/dx = g (k and g being constants)
..and I get the complementary function: y = A + Be^-kx
What would the suggested form of the particular solution be? "Cx" ?

 

[HallsofIvy]

Yes. In general, if what you would otherwise use as a complentary function already satisfies the homogeneous equation, multiply by x.
(And if THAT also satisfies the homogeneous equation, multiply by x again!)