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Separation of Variables

AP Calculus AB· difficulty 3/5

Solve dy/dx=xydy/dx = xy (y>0y > 0).

  • A

    y=x2/2y = x^2/2

  • B

    y=ex2/2+Cy = e^{x^2/2 + C}

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  • C

    y=ex2y = e^{x^2}

  • D

    y=ln⁡(x2/2)y = \ln(x^2/2)

Explanation

ln⁡y=x2/2+C⇒y=Aex2/2\ln y = x^2/2 + C \Rightarrow y = A e^{x^2/2} where A=eCA = e^C.

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