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Separation of Variables

AP Calculus AB· difficulty 3/5

Solve dy/dx=−ydy/dx = -y with y(0)=4y(0) = 4.

  • A

    y=4exy = 4 e^x

  • B

    y=4−x2y = 4 - x^2

  • C

    y=4e−xy = 4 e^{-x}

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  • D

    y=−4x+4y = -4 x + 4

Explanation

y=Ce−xy = C e^{-x}. y(0)=C=4y(0) = C = 4.

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