Question

Determine the order and degree of the given differential equation: $(\frac{d^{3}y}{dx^{3}})^{\frac{1}{6}}\cdotp (\frac{dy}{dx})^{\frac{1}{3}}=5$

Answer 1

Order 3 and power is 1

Answer 2

Answer:

The order of the differential equation is 3.

The degree of the differential equation is 1/6.

Step-by-step explanation:

The derivative with the highest order in a differential equation is the order of the differential equation.

The order of this differential equation is 3 because the highest order derivative is $\frac{d^{3} y}{dx^{3} }$ whereas the order of the other derivative $\frac{dy}{dx}$ is 1

The degree of the differential equation is the power of the derivative with the highest order present in the given differential equation.

The degree of this differential equation is 1/6 because the power of the highest order derivative  $\frac{d^{3} y}{dx^{3} }$ is 1/6