Question

The sum of the order and degree of differential equation \(2x^3\left(\frac{d^2y}{dx^2}\right)^4 + \frac{d^3y}{dx^3}+y=0\) is :

• A. 4
• B. 5
• C. 6
• D. not defined

Answer 1

The Correct Option is A

The given differential equation is \( 2x^3\left(\frac{d^2y}{dx^2}\right)^4 + \frac{d^3y}{dx^3} + y = 0 \).

Step 1: Identify the Order of the Differential Equation

The order of a differential equation is the highest derivative present in the equation. Here, the highest derivative is \(\frac{d^3y}{dx^3}\), which is the third derivative. Thus, the order is 3.

Step 2: Identify the Degree of the Differential Equation

The degree of a differential equation is the power of the highest order derivative when the equation is a polynomial in its derivatives. For the given equation, \(\frac{d^3y}{dx^3}\) is the highest order derivative and its degree is 1 because it is raised to the first power. Note that the term \(\left(\frac{d^2y}{dx^2}\right)^4\) does not determine the degree because the highest order derivative decides the degree when the equation is non-linear.

Step 3: Calculate the Sum of the Order and Degree

The sum of the order and degree is \(3 + 1 = 4\).

Therefore, the correct answer is 4.