I have this differential equation: $y'=-1+2xy$. I am asked to identify a curve that contains all possible minimum points of the various solution curves. Now I have no idea how to do this. The most I have done so far is set it to zero and I get $y=\frac{1}{2x}$. But I am not too sure how to use this or how to continue.
2026-04-04 00:54:36.1775264076
help with differential equations and local minimum
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What must be true about a function if it is differentiable and has a minimum? Fermat tells us the derivative is zero.
In this problem, you are given the derivative of any curve that solves the ode. You set it equal to zero and found the curve containing all of these potential minima. You are done.