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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
$\text{y}=\sin kt$ satisfies the differential equation $y\ "+\ 9y = 0$. Then $k$ :
  • ✓
    $\pm3$
  • B
    $0$
  • C
    $\pm2$
  • D
    $\pm4$
✓

Answer

Correct option: A.
$\pm3$
Given, $\text{y}=\sin kt$ satisfies the differential equation $y\ " + 9y = 0.$
Then, we have,$-\text{k}^2\sin\text{kt}+9\sin\text{kt}=0$ or,
$=\text{k}^2-9=0$
$[$Since $\sin\text{kt}\neq 0] $ or,
$=\text{k}=\pm3.$

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