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The easiest work-around I can think of is to write a "shell" for the current FourierTransform: ft[(h : List | Plus | Equal)[a__], t_, w_] := ft[#, t, w] & /@ h[a] ft[a_ b_, t_, w_] /; FreeQ[b, t] := b ft[a, t, w] ft[a_, t_, w_] := FourierTransform[a, t, w] ft[{a f[t] + b g'[t] == 0, c f'[t] + d e g[t] h[t] == 0}, t, w] {a FourierTransform[f[t], t, ...



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