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The equation \( \left(\dfrac{d^{2}y}{dx^{2}}\right)^{3} + \dfrac{dy}{dx} = 0 \) has order and degree

  • A.three and two
  • B.two and one
  • C.three and three
  • D.two and three

Answer: D

The highest derivative present is the second, so the order is two. That derivative appears cubed, so the degree is three. The first derivative's own power is irrelevant to the degree, which is read only from the highest-order term after the equation has been cleared of radicals and fractions in the derivatives

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