Form the differential equation for the family of curves y = A e^(3x) + B e^(−3x). A. d²y/dx² + 9y = 0 B. d²y/dx² − 9y = 0 C. d²y/dx² + 3y = 0 D. d²y/dx² − 3y = 0 Answer: B) d²y/dx² − 9y = 0 Explanation: y' = 3A e^(3x) − 3B e^(−3x). y'' = 9A e^(3x) + 9B e^(−3x) = 9(A e^(3x) + B e^(−3x)) = 9y. Hence, d²y/dx² − 9y = 0.

imo class 12 differential equations

Form the differential equation for the family of curves y = A e^(3x) + B e^(−3x).

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Form the differential equation for the family of curves y = A e^(3x) + B e^(−3x).

Answer: B) d²y/dx² − 9y = 0

Explanation: y' = 3A e^(3x) − 3B e^(−3x). y'' = 9A e^(3x) + 9B e^(−3x) = 9(A e^(3x) + B e^(−3x)) = 9y. Hence, d²y/dx² − 9y = 0.