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NDA 1 2024 Maths, question 75

Topic: Differential equations

Q75

What are the order and degree respectively of the differential equation {2−(dydx)2right}0.6=d2ydx2\text{\{}2-(\frac{dy}{dx})^{2}right\}^{0.6}=\frac{d^{2}y}{dx^{2}} ?

  1. (a) 2,22,2
  2. (b) 2,32,3
  3. (c) 5,25,2
  4. (d) 2,52,5Correct answer

Solution.

Answer: (d) 2,52,5

  1. The equation is [2−(dydx)2]0.6=d2ydx2\left[2 - \left(\frac{dy}{dx}\right)^{2}\right]^{0.6} = \frac{d^{2}y}{dx^{2}}, and 0.6=350.6 = \frac{3}{5}.
  2. Raise both sides to the power 5: [2−(dydx)2]3=(d2ydx2)5\left[2 - \left(\frac{dy}{dx}\right)^{2}\right]^{3} = \left(\frac{d^{2}y}{dx^{2}}\right)^{5}.
  3. The highest derivative is the second, so order 2; its power is 5, so degree 5.

Trap: The bracket is misprinted in the paper ("right}"); it is one bracket raised to the power 0.6.