The differential equation corresponding to the family of curves y = a cos x + b sin x is: A. d²y/dx² − y = 0 B. d²y/dx² + y = 0 C. dy/dx + y = 0 D. d²y/dx² + y² = 0 Answer: B) d²y/dx² + y = 0 Explanation: y' = −a sin x + b cos x. y'' = −a cos x − b sin x = −(a cos x + b sin x) = −y. Thus, d²y/dx² + y = 0.

imo class 12 differential equations

The differential equation corresponding to the family of curves y = a cos x + b sin x is:

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The differential equation corresponding to the family of curves y = a cos x + b sin x is:

Answer: B) d²y/dx² + y = 0

Explanation: y' = −a sin x + b cos x. y'' = −a cos x − b sin x = −(a cos x + b sin x) = −y. Thus, d²y/dx² + y = 0.