Question:
If p and q are the order and degree of the differential equation \(y\dfrac{dy}{dx} + x^3\dfrac{d^2y}{dx^2} + xy = \cos x\), then
यदि p और q अवकल समीकरण \(y\dfrac{dy}{dx} + x^3\dfrac{d^2y}{dx^2} + xy = \cos x\) की कोटि (order) और घात (degree) हैं, तो
Options:
- p = q
- p < q
- p > q
- p ≠ q
- p = q
- p < q
- p > q
- p ≠ q
Correct Answer: c)
Explanation:
Highest derivative is \(\dfrac{d^2y}{dx^2}\), so order \(p = 2\).
The power of the highest derivative is 1, so degree \(q = 1\).
Since \(p = 2\) and \(q = 1\), \(p > q\).
उच्चतम अवकलज \(\dfrac{d^2y}{dx^2}\) है, अतः कोटि \(p = 2\)। उच्चतम अवकलज की घात 1 है, अतः \(q = 1\)। अतः \(p > q\)।