NCERT Solutions
Class 12 - Mathematics Part-2 - Chapter 9: DIFFERENTIAL EQUATIONSExercise 9.1
Class 12 - Mathematics Part-2 - Chapter 9: DIFFERENTIAL EQUATIONS
Question. 1
Determine order and degree (if defined) of the differential equation \(\frac{d^4y}{dx^4} + \sin(y''') = 0\).
Answer:
Order 4; Degree not defined
Question. 2
Determine order and degree (if defined) of the differential equation \(y' + 5y = 0\).
Answer:
Order 1; Degree 1
Question. 3
Determine order and degree (if defined) of the differential equation \(\left(\frac{ds}{dt}\right)^4 + 3s\frac{d^2s}{dt^2} = 0\).
Answer:
Order 2; Degree 1
Question. 4
Determine order and degree (if defined) of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \cos\left(\frac{dy}{dx}\right) = 0\).
Answer:
Order 2; Degree not defined
Question. 5
Determine order and degree (if defined) of the differential equation \(\frac{d^2y}{dx^2} = \cos 3x + \sin 3x\).
Answer:
Order 2; Degree 1
Question. 6
Determine order and degree (if defined) of the differential equation \((y''')^2 + (y'')^3 + (y')^4 + y^5 = 0\).
Answer:
Order 3; Degree 2
Question. 7
Determine order and degree (if defined) of the differential equation \(y''' + 2y'' + y' = 0\).
Answer:
Order 3; Degree 1
Question. 8
Determine order and degree (if defined) of the differential equation \(y' + y = e^x\).
Answer:
Order 1; Degree 1
Question. 9
Determine order and degree (if defined) of the differential equation \(y'' + (y')^2 + 2y = 0\).
Answer:
Order 2; Degree 1
Question. 10
Determine order and degree (if defined) of the differential equation \(y'' + 2y' + \sin y = 0\).
Answer:
Order 2; Degree 1
Question. 11
The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \sin\left(\frac{dy}{dx}\right) + 1 = 0\) is
3
2
1
not defined
Question. 12
The order of the differential equation \(2x^2\frac{d^2y}{dx^2} - 3\frac{dy}{dx} + y = 0\) is
2
1
0
not defined