The order and degree of the differential equation
\[
\left[ \left( \frac{d^2 y}{dx^2} \right)^2 - 1 \right]^2 = \frac{dy}{dx} \text{ are, respectively:}
\]
Show Hint
- 2, 2
- 2, not defined
- 1, 2
- 2, not defined
The Correct Option is A
Solution and Explanation
To find the order and degree:
- The order is the highest derivative present in the equation. Here, the highest derivative is $\frac{d^2 y}{dx^2}$, so the order is 2.
- The degree is the power of the highest order derivative after removing all fractional powers and roots. The term $\left( \frac{d^2 y}{dx^2} \right)^2$ appears inside a square again, making it of power 2 × 2 = 4 originally.
But we observe it appears as $\left[ \left( \frac{d^2 y}{dx^2} \right)^2 - 1 \right]^2$.
So the degree with respect to the highest derivative (i.e., $d^2y/dx^2$) is 2.
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