- #1

TranscendArcu

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[itex]y' + p(x)y = g(x) y[/itex]

[itex]→ y' + y[(p + g)(x)] = 0[/itex]. I would then have,

[itex]Ω(x) = e^{\int (p + g)(x) dx}[/itex] and multiplying through,

[itex]Ω(x)y' + Ω(x)y[(p + g)(x)] = 0[/itex]

[itex]→ (Ω(x)y)' = 0 → Ω(x)y = 0[/itex]

But, this seems to be leading me to the conclusion that y = 0. Is that right or have I done something wrong? Is it possible to solve a Bernoulli equation with n=1 by constructing an integrating factor?