Question

The order and degree of the differential equation $\left(\frac{d^{3}y}{d{x}^3}\right)=2\frac{d^{2}y}{d{x}^2}+\sqrt[3]{co{s}^{2}x}$ 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)

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