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AP Calculus AB· difficulty 3/5

For dy/dx=x2+y2dy/dx = x^2 + y^2 (positive everywhere except origin), all solution curves are

  • A

    Increasing wherever (x,y)≠(0,0)(x, y) \ne (0, 0)

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  • B

    Constant

  • C

    Decreasing

  • D

    Periodic

Explanation

y′=x2+y2≥0y' = x^2 + y^2 \ge 0, with equality only at origin → solutions are increasing.

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