Types Of Differential Equations

Step 1: Concept
Degree is the power of the highest order derivative after removing radicals/fractions.
Step 2: Analysis
Square both sides to remove the fractional power: .
Step 3: Conclusion
The highest order derivative is and its power is 2. So, degree is 2.
Final Answer: (B)

The general equation of a parabola whose axis is along the x-axis is given by: Where is a constant. Differentiating both sides of this equation with respect to , we get:

Step 2: Differentiating again to find the second-order equation.
Differentiating again: Simplifying:

Step 3: Conclusion.
This is a second-order differential equation, and the highest power of the highest order derivative is 1, meaning the degree is 1. Therefore, the correct degree and order are 2 and 1, respectively.

Step 1: Formula / Definition}

Step 2: Calculation / Simplification}
Given

Substitute into equation:



Step 3: Final Answer