If m is the degree and n is the order of the given differential equation
\(\frac{x^3\left(\frac{d^3 y}{d x^3}\right)^2+2 x^2\left(\frac{d^2 y}{d x^2}\right)^3}{(x+1)^5}=\left(3 x-\frac{d^2 y}{d x^2}\right)^4 \)
Answer & explanation
Correct answer: option 2
\(\frac{x^3\left(\frac{d^3 y}{d x^3}\right)^2+2 x^2\left(\frac{d^2 y}{d x^2}\right)^3}{(x+1)^5}=\left(3 x-\frac{d^2 y}{d x^2}\right)^4 \)
$⇒x^3(\frac{d^3 y}{d x^3})^2+2x^2(\frac{d^2 y}{d x^2})^3-(x+1)^5(3x-\frac{d^2 y}{d x^2})^4=0$
∴ order (n) = 3
Degree (m) = 2
∴ m + n = 5
option 2 is correct.