If \( p \) and \( q \) are degree and order of the differential equation \( \left(\displaystyle\frac{d^2y}{dx^2}\right)^3-2\left(\displaystyle\frac{dy}{dx}\right)^4=6 \) respectively. Then the value of \( 2p+3q \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12
The highest derivative is \( \frac{d^2y}{dx^2} \), so the order is q = 2.
The power of this highest derivative is 3, so the degree is p = 3.
\( 2p+3q=2(3)+3(2)=12 \)
Why the other options are incorrect
Option (1) 13 — Incorrect. This comes from taking p = 2 and q = 3, i.e. interchanging degree and order.
Option (3) 11 — Incorrect. With p = 3 and q = 2 the value is 12, not 11.
Option (4) 14 — Incorrect. This takes the degree as 4, the power of \( \frac{dy}{dx} \). The degree is the power of the highest derivative \( \frac{d^2y}{dx^2} \), which is 3.