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Order of DE obtained by eliminating constants A, B from y = A e^x + B e^(-x):

A0
B2 (two constants → 2nd-order DE: y'' = y)
C1
D3
Answer & Solution
Correct answer: B. 2 (two constants → 2nd-order DE: y'' = y)
y' = A e^x - B e^(-x). We have y'' = A e^x + B e^(-x). So y'' = y. So y'' - y = 0 (order 2). **General rule:** n arbitrary constants → DE of order n.
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