# First order differential eqn dy/dx + Py = Qy^n

1. Mar 4, 2014

### tony24810

show that the substitution z = y^-(n-1) transforms the general equation dy/dx + Py = Qy^n, where P and Q are functions of x, into the linear equation dz/dx - P(n-1)z = -Q(n-1). (Bernoulli's equation)

Well, I looked up Bernoulli's stuff on internet, found the usual air flow equation but not this one. In fact I followed the standard procedure to transform the equation, but what I got is a whole bunch of fraction rather than just the -(n-1).

2. Mar 4, 2014

### tony24810

never mind

i managed to solved it myself, please ignore this post. i actually made mistake in my differentiation with the negative indices.

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