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Assume that the function V (S, I, t) satisfies the PDE av av 1 a2 v av + In S +-02 at osz trs - rV = 0. 2 as Consider the change of variables V (S, I, t) = F(y, t), where I+(T - t) InS y = TShow that F(y, t) satisfies the following PDE: OF 02 (T - t)2 82 F 02 T - tOF -rF = 0. at 2T2 r 2 T dy