Question

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

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

Answer 1

Answer: (B)

$m=3,n=2$

The given differential equation can be rewritten as
${\left(\frac{d^{2}y}{d{x}^2}\right)}^5\cdot \frac{d^{3}y}{d{x}^3}+4{\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{d^{3}y}{d{x}^3}\right)}^2$
$=(x^2-1)\frac{d^{3}y}{d{x}^3}\Rightarrow$ order $\left(m\right)$ $=3$
and degree $\left(n\right)=2$