Question:
The order and degree of the differential equation
\[
y=\left(\frac{d^2y}{dx^2}\right)^2-\lambda\frac{dy}{dx}
\]
is:
The order and degree of the differential equation
\[
y=\left(\frac{d^2y}{dx^2}\right)^2-\lambda\frac{dy}{dx}
\]
is:
Show Hint
Order is always defined for any differential equation. Degree is defined only if the equation can be written as a polynomial in its derivatives. Always check the power of the highest derivative for degree.
Updated On: Sep 11, 2026
- Order = 2, Degree = 2
- Order = 2, Degree = 3
- Order = 1, Degree = 2
- Order = 2, Degree = 4
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The Correct Option is A
Solution and Explanation
Concept:
• Order of a differential equation is the order of the highest derivative occurring in it.
• Degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in its derivatives.
Step 1: Identify the highest order derivative
Look at the terms involving derivatives in the equation:
\[ y = \left( \frac{d^2y}{dx^2} \right)^2 - \lambda \left( \frac{dy}{dx} \right) \]
The derivatives present are \( \frac{d^2y}{dx^2} \) (second order) and \( \frac{dy}{dx} \) (first order).
The highest order is 2. So, Order = 2.
Step 2: Determine the degree of the equation
Identify the term containing the highest order derivative, which is \( \left( \frac{d^2y}{dx^2} \right)^2 \).
The power to which this highest order derivative is raised is 2.
Since the equation is already in polynomial form with respect to derivatives (no fractional powers or derivatives inside transcendental functions), this power is the degree.
So, Degree = 2.
• Order of a differential equation is the order of the highest derivative occurring in it.
• Degree of a differential equation is the power of the highest order derivative when the equation is expressed as a polynomial in its derivatives.
Step 1: Identify the highest order derivative
Look at the terms involving derivatives in the equation:
\[ y = \left( \frac{d^2y}{dx^2} \right)^2 - \lambda \left( \frac{dy}{dx} \right) \]
The derivatives present are \( \frac{d^2y}{dx^2} \) (second order) and \( \frac{dy}{dx} \) (first order).
The highest order is 2. So, Order = 2.
Step 2: Determine the degree of the equation
Identify the term containing the highest order derivative, which is \( \left( \frac{d^2y}{dx^2} \right)^2 \).
The power to which this highest order derivative is raised is 2.
Since the equation is already in polynomial form with respect to derivatives (no fractional powers or derivatives inside transcendental functions), this power is the degree.
So, Degree = 2.
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