Question

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

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

Answer 1

The correct option is B $m=3,n=2$

The given differential equation can be written as ${\left(\frac{d^{3}y}{d{x}^3}\right)}^2-(x^2-1)\frac{d^{3}y}{d{x}^3}+\left(\frac{d^{3}y}{d{x}^3}\right){\left(\frac{d^{2}y}{d{x}^2}\right)}^5+4{\left(\frac{d^{2}y}{d{x}^2}\right)}^3=0$
Clearly, its order is $3$ and degree is $2$.
Therefore, $m=3$ and $n=2$.