Form of f(x) | ‘Test form’ of p.i | Notes |
p | λ | p is a given constant λ is a constant to be found |
p + qx | λ + μx | p & q are given constants λ & μ are constants to be found Use the full test form of the p.i., even if there is no constant term (i.e., even if p = 0) |
p + qx + rx2 | λ + μx + νx2 | p, q & r are given constants λ, μ & ν are constants to be found Use the full test form of the p.i., even if there is no constant or x term (i.e., even if p = 0 and/or q =0) |
pekx | λekx | k & p are given constants λ is a constant to be found |
p cos ωx + q sin ωx | λ cos ωx + μ sin ωx | p, q & ω are given constants λ & μ are constants to be found Use the full test form of the p.i., even if f(x) only contains sin or only contains cos (i.e., even if p = 0 or q =0) |
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