Question

The “order” of the following ordinary differential equation is __________.
\[ \frac{d^3 y}{dx^3} + \left( \frac{d^2 y}{dx^2} \right)^6 + \left( \frac{dy}{dx} \right)^4 + y = 0 \]

Hint:

The order is the highest derivative present, and degree is the power of that derivative (in polynomial form).

Answer 1

Correct Answer: 3

The order of a differential equation is determined by the highest derivative present. Here, the highest order derivative is: \[ \frac{d^3 y}{dx^3} \Rightarrow {Order} = 3 \] The degree is the highest power to which the highest order derivative is raised, provided the equation is polynomial in derivatives. In this case: \[ \left( \frac{d^3 y}{dx^3} \right)^1 \Rightarrow {Degree} = 1 \] So, order = 3 and degree = 1.