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Verifying Solutions for Differential Equations

AP Calculus AB· difficulty 2/5

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

  • A

    y=2exy = 2 e^x

  • B

    y=e2xy = e^{2x}

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  • C

    y=2xy = 2x

  • D

    y=ex/2y = e^{x/2}

Explanation

y′=2e2x=2yy' = 2 e^{2x} = 2 y. (Note: any constant multiple Ce2xC e^{2x} works, including C=2C = 2 in option D — but option B is the simplest verification.)

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AP Calculus AB · Verifying Solutions for Differential Equations Practice Question | Acemy