Question:
The order and degree of the differential equation \[ 1+\left(\frac{d^3y}{dx^3}\right)^3 = \lambda \frac{d^2y}{dx^2} \] is:
The order and degree of the differential equation \[ 1+\left(\frac{d^3y}{dx^3}\right)^3 = \lambda \frac{d^2y}{dx^2} \] is:
Show Hint
Always look for the 'boss' derivative first to find the order. The degree is just the power that 'boss' derivative is raised to.
Ensure the equation is free of fractional powers of derivatives before determining the degree.
Ensure the equation is free of fractional powers of derivatives before determining the degree.
Updated On: Sep 11, 2026
- Order = \( 3 \), Degree = \( 3 \)
- Order = \( 2 \), Degree = \( 2 \)
- Order = \( 3 \), Degree = \( 1 \)
- Order = \( 2 \), Degree = \( 1 \)
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The Correct Option is A
Solution and Explanation
Concept:
• Order: The highest order derivative present in the differential equation.
• Degree: The power of the highest order derivative when the equation is a polynomial in derivatives (free from radicals and fractions).
Step 1: Identify the highest order derivative
The derivatives present are:
• Third order: \( \frac{d^3y}{dx^3} \)
• Second order: \( \frac{d^2y}{dx^2} \) The highest order is \( 3 \). Thus, Order = \( 3 \).
Step 2: Check for polynomial form and find the degree
The equation is already in polynomial form with respect to its derivatives. The highest order derivative term is \( \left( \frac{d^3y}{dx^3} \right)^3 \). The exponent (power) of this highest order derivative is \( 3 \). Thus, Degree = \( 3 \).
Step 3: Conclusion
Order = \( 3 \) and Degree = \( 3 \). This matches option (A).
• Order: The highest order derivative present in the differential equation.
• Degree: The power of the highest order derivative when the equation is a polynomial in derivatives (free from radicals and fractions).
Step 1: Identify the highest order derivative
The derivatives present are:
• Third order: \( \frac{d^3y}{dx^3} \)
• Second order: \( \frac{d^2y}{dx^2} \) The highest order is \( 3 \). Thus, Order = \( 3 \).
Step 2: Check for polynomial form and find the degree
The equation is already in polynomial form with respect to its derivatives. The highest order derivative term is \( \left( \frac{d^3y}{dx^3} \right)^3 \). The exponent (power) of this highest order derivative is \( 3 \). Thus, Degree = \( 3 \).
Step 3: Conclusion
Order = \( 3 \) and Degree = \( 3 \). This matches option (A).
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