Question

For the equation \[ \frac{d^3 y}{dx^3} + x \left( \frac{dy}{dx} \right)^{3/2} + x^2 y = 0 \] the correct description is

• A. an ordinary differential equation of order 3 and degree 2.
• B. an ordinary differential equation of order 3 and degree 3.
• C. an ordinary differential equation of order 2 and degree 3.
• D. an ordinary differential equation of order 3 and degree 3/2.

Hint:

To determine the order of a differential equation, identify the highest derivative. The degree is the exponent of the highest derivative when written in polynomial form.

Answer 1

The Correct Option is A

The given equation is: \[ \frac{d^3 y}{dx^3} + x \left( \frac{dy}{dx} \right)^{3/2} + x^2 y = 0 \] To determine the order and degree of the differential equation: - The order of a differential equation is the highest derivative present. Here, the highest derivative is \(\frac{d^3 y}{dx^3}\), which is of order 3. - The degree of a differential equation is the power of the highest derivative when the equation is expressed in a polynomial form with respect to the derivatives. In this equation, the term \(\left( \frac{dy}{dx} \right)^{3/2}\) has an exponent of \(3/2\), which means the degree is 2 when the equation is in a polynomial form. Thus, the correct description is that this is an ordinary differential equation of order 3 and degree 2, corresponding to option (A).