Question

Find the order and degree of the differential equation ${\left(\frac{d^{4}y}{d{x}^4}\right)}^{3/5}-5\frac{d^{3}y}{d{x}^3}+6\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+5=0$

• A. $4,3$
• B. $3,4$
• C. $4,5$
• D. $5,4$

Answer 1

Answer: (A)

${\left(\frac{d^{4}y}{d{x}^4}\right)}^{3/5}-5\frac{d^{3}y}{d{x}^3}+6\frac{d^{2}y}{d{x}^2}-8\frac{dy}{dx}+5=0$
$\Rightarrow$ ${\left(\frac{d^{4}y}{d{x}^4}\right)}^3={\left(5\frac{d^{3}y}{d{x}^3}-6\frac{d^{2}y}{d{x}^2}+8\frac{dy}{dx}-5\right)}^5$
Which is the differential equation of order $4$ and degree $3$ . (because order is equal to highest order derivative and degree is equal to highest power of highest order derivative).