Question: Example: Consider y = y. Two solutions are y1 = et and yz = et+2. Is the general solution then y = cle + coet+

Example: Consider y" = y. Two solutions are y1 = et and yz = et+2. Is the general solution then y = cle + coet+ 2 ? NO! Note that for any KER, et+K Note is NOT uniquely = ek. et + expressed as also , ettk = 0. et aet+ bett z + e K - 2 t + 2 Subtracting, we obtain 0 = - e et + 1 0 + 2 a linear combination of y , andy , that is identically zero . NOT zero

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