Question

The order and degree of the differential equation ${\left(\frac{d^{3}y}{d{x}^3}\right)}^{1/3}=2\frac{d^{2}y}{d{x}^2}+\sqrt[3]{3{\cos }^{2}x}$ are, respectively :

• A. $3$ and $1$
• B. $3$ and $3$
• C. $1$ and $3$
• D. $3$ and $2$
• E. $2$ and $2$

Answer 1

Answer: (A)

$3$ and $1$

Given differential equation is
${\left(\frac{d^{3}y}{d{x}^3}\right)}^{1/3}=2\frac{d^{2}y}{d{x}^2}+\sqrt[3]{3{\cos }^{2}x}$
On cubing both sides, we get
$\left(\frac{d^{3}y}{d{x}^3}\right)={(2\frac{d^{2}y}{d{x}^2}+\sqrt[3]{3{\cos }^{2}x})}^3$
Here, we see that the highest order derivative is $3$ and whose degree is $1.$