If m and n are respectively the order and the degree of the differential equation \(x\left(\displaystyle\frac{d^4y}{dx^4}\right)^3 + \left(\displaystyle\frac{d^2y}{dx^2}\right)^5 - y = e^{x}\), then mn is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 12
The order is the order of the highest derivative present, and the degree is the power of that highest derivative.
The highest derivative present is \(\frac{d^4y}{dx^4}\), so
\(m = 4\)
It appears with power 3, so
\(n = 3\)
The power 5 belongs to \(\frac{d^2y}{dx^2}\), which is not the highest derivative, so it does not decide the degree.
\(mn = 4 \times 3 = 12\)