Differential Equations
Order and Degree
IIT-JEE 2010
Grade 12
Question:
The order and degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \cos\left(\frac{dy}{dx}\right) = 0$ are:
(1) order 2, degree 2
(2) order 1, degree not defined
(3) order 2, degree not defined
(4) order 2, degree 1
Step-by-Step Solution
Key Concept: Check whether the equation can be written as a polynomial in derivatives — note carefully what the presence of $\cos(\frac{dy}{dx})$ does to the notion of "degree".
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)