Differential Equations

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Locate the bifurcation values of a for the one-parameter family and describe the bifurcation that takes place at each such value.
dy/dt=e^(-y^2)+a
I got that the equilibrium points will be at -sqrt(ln(a)). I don't know if that is fine. I took the partial derivative with respect to y and got -2ye^(-y^2) and that is zero when a is 0 if I plug in -sqrt(ln(a)) as y.

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