What are the order and degree respectively of the differential equation \left\{2-\left(\frac{dy}{dx}\right)^{2}\right\}^{0.6}=\frac{d^{2}y}{dx^{2}} ?
- A. 2, 2
- B. 2, 3
- C. 5, 2
- D. 2, 5 ✓
Correct Answer: D. 2, 5
Explanation
Rewrite the equation as (2 - (y')^2)^{\frac{3}{5}} = y''. Raising both sides to the power of 5 gives (2 - (y')^2)^3 = (y'')^5. The highest order derivative is y'' (order 2), and its highest power in the polynomial form is 5 (degree 5).
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