Question:
Identify the order and degree of the differential equation:
\[
\left(\frac{d^3y}{dx^3}\right)^2 + 4\left(\frac{dy}{dx}\right)^4 + y = \sin(x)
\]
Identify the order and degree of the differential equation:
\[
\left(\frac{d^3y}{dx^3}\right)^2 + 4\left(\frac{dy}{dx}\right)^4 + y = \sin(x)
\]
Show Hint
Degree is always determined using the highest order derivative only, not by the largest exponent appearing elsewhere in the equation.
Updated On: Jun 3, 2026
- \( \text{Order } 3, \text{Degree } 4 \)
- \( \text{Order } 3, \text{Degree } 2 \)
- \( \text{Order } 4, \text{Degree } 3 \)
- \( \text{Order } 1, \text{Degree } 4 \)
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
The order of a differential equation is the order of the highest derivative present. The degree is the exponent of the highest order derivative after removing radicals and fractions involving derivatives.
Step 1: Find the highest order derivative.
The highest derivative present is: \[ \frac{d^3y}{dx^3} \] Hence, the order is: \[ 3 \]
Step 2: Determine the degree.
The highest order derivative appears as: \[ \left(\frac{d^3y}{dx^3}\right)^2 \] Therefore, the degree is: \[ 2 \]
Step 1: Find the highest order derivative.
The highest derivative present is: \[ \frac{d^3y}{dx^3} \] Hence, the order is: \[ 3 \]
Step 2: Determine the degree.
The highest order derivative appears as: \[ \left(\frac{d^3y}{dx^3}\right)^2 \] Therefore, the degree is: \[ 2 \]
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