Question

The order and degree of ${(\frac{d^{4}y}{{dx}^4}+\frac{d^{2}y}{{dx}^2})}^{5/2}=a\frac{d^{2}y}{{dx}^2}$ are $p,q$ then $p+q=$

• A. $9$
• B. $6$
• C. $7$
• D. $10$

Answer 1

The correct option is A $9$

${\left(\frac{d^{4}y}{d{x}^4}+\frac{d^{2}y}{d{x}^2}\right)}^{5/2}=a\frac{d^{2}y}{d{x}^2}$

Let order is $p$ and degree is $q$.

order is highest derivative,

therefore,

$p=4$

and, the degree is power raised to the highest derivative of differentiation,

if we open the bracket $\frac{d^{4}y}{d{x}^4}$ get the power $\frac{5}{2}$

Hence the degree is $\frac{5}{2}$

Therefore,

$q=\frac{5}{2}$

Now,

$p+q=4+\frac{5}{2}=\frac{13}{2}$