Question

The order and degree of the following differential equation are, respectively: \[ \frac{d^4y}{dx^4} + 2 \frac{d^2y}{dx^2} + y^2 = 0. \]

• A. -4, 1
• B. 4, not defined
• C. 1, 1
• D. 4, 1

Hint:

To find the order and degree, look for the highest derivative for the order and the exponent of that derivative for the degree.

Answer 1

The Correct Option is D

The given equation is: \[ \frac{d^4y}{dx^4} + 2 \frac{d^2y}{dx^2} + y^2 = 0. \] - Order: The order of a differential equation is the highest derivative of the unknown function (in this case, $y$). The highest derivative here is $\frac{d^4y}{dx^4}$, so the order is 4. - Degree: The degree is the exponent of the highest order derivative after removing any fractions or radicals. Here, the highest derivative is $\frac{d^4y}{dx^4}$ and its exponent is 1 (no powers of the derivative). Therefore, the degree is 1. Thus, the order is 4 and the degree is 1.