Let the degree and order of the differential equation \(2x^3\displaystyle\frac{dy}{dx} - 5\left(\frac{d^2y}{dx^2}\right)^2 = 6\left(\frac{dy}{dx}\right)^3\) be m and n respectively. Then
(A) \(m = 2\)
(B) \(n = 3\)
(C) \(m = 3\)
(D) \(mn = 4\)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (D) only
The highest derivative present is \(\frac{d^2y}{dx^2}\), so the order is
\(n = 2\)
The equation is a polynomial in the derivatives. The degree is the highest power of the highest order derivative \(\frac{d^2y}{dx^2}\), which appears as \(\left(\frac{d^2y}{dx^2}\right)^2\):
\(m = 2\)
So \(m = 2\) and \(n = 2\).
Checking the statements
(A) \(m = 2\) — Correct. The degree m is 2.
(B) \(n = 3\) — Incorrect. The order n is 2; there is no third derivative.
(C) \(m = 3\) — Incorrect. 3 is the power of \(\frac{dy}{dx}\), which is not the highest order derivative.
(D) \(mn = 4\) — Correct. \(mn = 2 \times 2 = 4\).