Question

If $m$ and $n$ are order and degree of the equation

${\left(\frac{d^{2}y}{d{x}^2}\right)}^5+4\frac{\left(\frac{d^{2}y}{d{x}^2}\right)}{\left(\frac{d^{3}y}{d{x}^3}\right)}+\left(\frac{d^{3}y}{d{x}^3}\right)=x^2-1$ then $(m,n)=$

• A. $(3,3)$
• B. $(3,2)$
• C. $(3,5)$
• D. $(3,1)$

Answer 1

The correct option is B $(3,2)$

Given equation can be written as

$y_2^5+\frac{4y_2}{y_3}+y_3=(x^2-1)$

$\Rightarrow y_3{y}_2^5+4y_2+y_3^2-(x^2-1)y_3=0$

$\Rightarrow$ Order $=3$ (Order of a differential equation is the order of the highest derivative (also known as differential coefficient) present in the equation.)
Degree $=2$ (The degree of differential equation is represented by the power of the highest order derivative in the given differential equation.)