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Higher Order Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsHigher Order Derivatives1 Mark
MCQ
If $\text{y}=\text{a}\sin\text{mx}+\text{b}\cos\text{mx},$ then $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is equal to :
  • ✓
    $-m^2y$
  • B
    $m^2y$
  • C
    $-my$
  • D
    $my$
✓

Answer

Correct option: A.
$-m^2y$
$\text{y}=\text{a}\sin\text{mx}+\text{b}\cos\text{mx}$
$\frac{\text{dy}}{\text{dx}}=\text{am}\cos\text{mx}-\text{bm}\sin\text{mx}$
$\frac{\text{d}^2\text{y}}{\text{dx}^2}=-\text{am}^2\sin\text{mx}-\text{bm}^2\cos\text{mx}=-\text{m}^2\text{y}$

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