Question

If $m$ and $n$ are the order and degree of the differential equation
${\left(\frac{d^{2}y}{d{x}^2}\right)}^5+4\frac{{\left(\frac{d^{2}y}{d{x}^2}\right)}^3}{\left(\frac{d^{2}y}{d{x}^2}\right)}+\frac{d^{2}y}{d{x}^2}=x^2-1$, then

• A. $m=3,n=3$
• B. $m=2,n=6$
• C. $m=3,n=5$
• D. $m=3,n=1$

Answer 1

Answer: (B)

$m=2,n=6$

Given differential can be written as

${\left(\frac{d^{2}y}{d{x}^2}\right)}^6+4{\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{d^{2}y}{d{x}^2}\right)}^2-(x^2-1)\left(\frac{d^{2}y}{d{x}^2}\right)=0$

Hence, $m=2$ and $n=6$