Question

If the order and degree of a differential equation $(\frac{d^4y}{dt^4} + \frac{d^2y}{dt^2})^{5/2} = 10 \frac{d^3y}{dt^3}$ are $p$ and $q$, respectively, then $p+q =$

• A. 9
• B. 6
• C. 7
• D. 10

Hint:

Always clear fractional powers (radicals) from the derivatives before identifying the degree of a differential equation.

Answer 1

The Correct Option is A

Step 1: Concept
Order is the highest derivative present. Degree is the power of the highest derivative after removing radicals.

Step 2: Meaning
Square both sides to eliminate the fractional power: $(\frac{d^4y}{dt^4} + \frac{d^2y}{dt^2})^5 = (10 \frac{d^3y}{dt^3})^2$.

Step 3: Analysis
The highest derivative is $\frac{d^4y}{dt^4}$, so order $p = 4$. After squaring, the power of this highest derivative is 5, so degree $q = 5$.

Step 4: Conclusion
Therefore, $p + q = 4 + 5 = 9$. Final Answer: (A)