Let the degree and order of the differential equation $2x^3\frac{dy}{dx}-5(\frac{d^2y}{dx^2})^2 = 6 (\frac{dy}{dx})^3$ 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
Given differential equation
$2x^3\frac{dy}{dx}-5\left(\frac{d^2y}{dx^2}\right)^2=6\left(\frac{dy}{dx}\right)^3$
Highest order derivative present is $\frac{d^2y}{dx^2}$
Hence order $n=2$
Degree is the power of the highest order derivative when the equation is free from radicals and fractions in derivatives
Here highest order derivative $\frac{d^2y}{dx^2}$ is raised to power $2$
Hence degree $m=2$
Check options
(A) $m=2$ True
(B) $n=3$ False
(C) $m=3$ False
(D) $mn=2\times2=4$ True
The correct options are (A) and (D).