Question:
The order and degree of the differential equation
\[
\left[2\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 \right]^{\frac{3}{2}} = \frac{d^3y}{dx^3}
\]
The order and degree of the differential equation
\[ \left[2\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 \right]^{\frac{3}{2}} = \frac{d^3y}{dx^3} \]
Show Hint
Always remove radicals/fractions before determining degree.
Updated On: May 8, 2026
- 2 and 2
- 2 and 1
- 3 and 2
- 3 and 3
- 2 and 4
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The Correct Option is C
Solution and Explanation
Concept:
• Order = highest order derivative
• Degree = power of highest order derivative (after removing radicals)
Step 1: Identify order
Highest derivative: \[ \frac{d^3y}{dx^3} \] Thus order = 3
Step 2: Remove fractional power
\[ \left[2y'' + (y')^2\right]^{3/2} = y''' \] Square both sides: \[ \left[2y'' + (y')^2\right]^3 = (y''')^2 \]
Step 3: Identify degree
Highest order derivative = \(y'''\) Power = 2 Thus degree = 2 Final Answer: \[ \boxed{3 \text{ and } 2} \]
• Order = highest order derivative
• Degree = power of highest order derivative (after removing radicals)
Step 1: Identify order
Highest derivative: \[ \frac{d^3y}{dx^3} \] Thus order = 3
Step 2: Remove fractional power
\[ \left[2y'' + (y')^2\right]^{3/2} = y''' \] Square both sides: \[ \left[2y'' + (y')^2\right]^3 = (y''')^2 \]
Step 3: Identify degree
Highest order derivative = \(y'''\) Power = 2 Thus degree = 2 Final Answer: \[ \boxed{3 \text{ and } 2} \]
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