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The question I'm trying to solve is part (ii) of the attached file

I've used partial derivatives to input back into the Black Scholes equations and after factorising it, I've got it down to:

(a + 2bt + αt +r) * (S².c.e^(at+bt²) = 0

I'm now stuck on what to do next, as there would need to be 2 equations in order to solve simultaneously which isn't the case above.

Help would appreciated

I've used partial derivatives to input back into the Black Scholes equations and after factorising it, I've got it down to:

(a + 2bt + αt +r) * (S².c.e^(at+bt²) = 0

I'm now stuck on what to do next, as there would need to be 2 equations in order to solve simultaneously which isn't the case above.

Help would appreciated