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here's the question: $$ u \frac{ \partial u}{ \partial x} = \rho \frac{ d P}{ d x}$$ may i generally state $$ \rho P+1/2 u^2 = const. $$

the book does, and it seems the [itex]dx[/itex] cancels the [itex]\partial x[/itex] on both sides and we simply integrate through. this seems to be mathematically untrue. can someone confirm/reject this? also, what conditions would be necessary to have the above true (if it is indeed untrue generally)?

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# Simple ODE/PDE clarification

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