Does y = \sin x satisfy y'' + y = 0?

Answer: Yes y'' = -\sin x. y'' + y = -\sin x + \sin x = 0. ✓

Which is a solution to dy/dx = 2y?

Answer: y = e^{2x} y' = 2 e^{2x} = 2 y. (Note: any constant multiple C e^{2x} works, including C = 2 in option D — but option B is the simplest verification.)

AP Calculus AB · Topic 7.2

Verifying Solutions for Differential Equations Practice

Part of Differential Equations.(FUN-7.B)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$y = \sin x$
- A
  $[0, \pi]$
- B
  $Yes$
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- C
  $No$
- D
  $x = 0$
Why
$y'' = -\sin x$
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Sample 2difficulty 2/5
$dy/dx = 2y$
- A
  $y = 2 e^x$
- B
  $y = e^{2x}$
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- C
  $y = 2x$
- D
  $y = e^{x/2}$
Why
$y' = 2 e^{2x} = 2 y$
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