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Verifying Solutions for Differential Equations

AP Calculus AB· difficulty 2/5

Does y=sin⁡xy = \sin x satisfy y′′+y=0y'' + y = 0?

  • A

    Only on [0,π][0, \pi]

  • B

    Yes

    check_circle
  • C

    No

  • D

    Only at x=0x = 0

Explanation

y′′=−sin⁡xy'' = -\sin x. y′′+y=−sin⁡x+sin⁡x=0y'' + y = -\sin x + \sin x = 0. ✓

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