Solve the initial value problem $xy'=y(xy-1), y(e^{-1})=e$
I was given the hint to use the substitution, but don't know how to find the proper substitution. What's the general rule of thumb in finding a substitution?
2026-03-26 17:30:35.1774546235
Solve the initial value problem $xy'=y(xy-1), y(e^{-1})=e$
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$$xy'=y(xy-1), y(e^{-1})=e$$ $$xy'+y=xy^2$$ Since $(xy)'=y'x+y$ $$(xy)'=\frac {(xy)^2}x$$ Can you take it from here ?