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Separation of Variables

AP Calculus AB· difficulty 2/5

Which DE is separable?

  • A

    dy/dx=x+ydy/dx = x + y

  • B

    dy/dx=exsin⁡ydy/dx = e^x \sin y

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  • C

    dy/dx=cos⁡(x+y)dy/dx = \cos(x + y)

  • D

    dy/dx=xy+1dy/dx = x y + 1

Explanation

dy/sin⁡y=ex dxdy/\sin y = e^x\,dx — separates into product of xx-only and yy-only terms.

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