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GATE 2023 MT – Question 13

Engineering Mathematics · Differential equations · 1 mark · Multiple choice

The order O and degree D of $(dy/dx)^3=\sqrt{d^2y/dx^2+10}$ are

  1. O = 2 and D = 1
  2. O = 1 and D = 2
  3. O = 6 and D = 1
  4. O = 2 and D = 6

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Correct answer: (A) O = 2 and D = 1

Explanation

Squaring removes the radical: $(y^\prime)^6=y^{\prime\prime}+10$. The highest derivative is second order and has first power.

Thus **order 2, degree 1, A**. The sixth power applies to the lower-order derivative.