GreenFunction

GreenFunction[{ℒ[u[x]], ℬ[u[x]]}, u, {x, xmin, xmax}, y] gives a Green's function for the linear differential operator ℒ with boundary conditions ℬ in the range xmin to xmax.

GreenFunction[{ℒ[u[x1, x2, ...]], ℬ[u[x1, x2, ...]]}, u, {x1, x2, ...} ∈ Ω, {y1, y2, ...}] gives a Green's function for the linear partial differential operator ℒ over the region Ω.

GreenFunction[{ℒ[u[x, t]], ℬ[u[x, t]]}, u, {x, xmin, xmax}, t, {y, τ}] gives a Green's function for the linear time-dependent operator ℒ in the range xmin to xmax.

GreenFunction[{ℒ[u[x1, ..., t]], ℬ[u[x1, ..., t]]}, u, {x1, ...} ∈ Ω, t, {y1, ..., τ}] gives a Green's function for the linear time-dependent operator ℒ over the region Ω.

Examples

GreenFunction[{y''[x] - y[x], y[0] == 0, y[1] == 0}, y, {x, 0, 1}, s]

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