Question:
The degree of the differential equation
\[ \left[1 + \left(\frac{dy}{dx}\right)^2 \right]^{3/2} = \frac{d^2 y}{dx^2} \]
is ______.
The degree of the differential equation
\[ \left[1 + \left(\frac{dy}{dx}\right)^2 \right]^{3/2} = \frac{d^2 y}{dx^2} \]
is ______.
Show Hint
Always remove radicals before determining degree.
Updated On: Apr 30, 2026
- \(1\)
- \(2\)
- \(3\)
- \(4\)
- \(5\)
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
Degree = power of highest order derivative after removing radicals/fractions.
Step 1: Given equation. \[ \left[1+\left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2} \]
Step 2: Remove fractional power. Square both sides: \[ \left[1+\left(\frac{dy}{dx}\right)^2\right]^3 = \left(\frac{d^2y}{dx^2}\right)^2 \]
Step 3: Identify highest order derivative. Highest derivative = \( \frac{d^2y}{dx^2} \) Its power = \(2\)
Step 4: Conclusion. \[ \text{Degree} = 2 \]
Step 1: Given equation. \[ \left[1+\left(\frac{dy}{dx}\right)^2\right]^{3/2} = \frac{d^2y}{dx^2} \]
Step 2: Remove fractional power. Square both sides: \[ \left[1+\left(\frac{dy}{dx}\right)^2\right]^3 = \left(\frac{d^2y}{dx^2}\right)^2 \]
Step 3: Identify highest order derivative. Highest derivative = \( \frac{d^2y}{dx^2} \) Its power = \(2\)
Step 4: Conclusion. \[ \text{Degree} = 2 \]
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