Order and Degree of DEs PYQs
Practice Class 12 CBSE Board Previous Year Questions (2008-2026)
Q1
2012 Board
00:00
Find the order and degree of $(\frac{d^2y}{dx^2})^3 + (\frac{dy}{dx})^2 + y = 0$. 1 Mark
Step 1: Identify Order
The highest order derivative present is $\frac{d^2y}{dx^2}$, which is second order.
Step 2: Identify Degree
The degree is the power of the highest order derivative. Here, the power is 3.
Order = 2, Degree = 3.
Order = 2, Degree = 3
Q2
2017 Board
00:00
Find the order and degree of $[1 + (\frac{dy}{dx})^2]^{3/2} = \frac{d^2y}{dx^2}$. 2 Marks
Step 1: Eliminate Radicals
Square both sides to remove the fractional power: $[1 + (\frac{dy}{dx})^2]^3 = (\frac{d^2y}{dx^2})^2$.
Step 2: Identify Order
Highest order derivative is $\frac{d^2y}{dx^2}$. Order = 2.
Step 3: Identify Degree
The power of the highest order derivative is 2. Degree = 2.
Order = 2, Degree = 2
Q3
2023 Board
00:00
Find the order and degree of $(\frac{d^3y}{dx^3})^2 + (\frac{dy}{dx})^3 = 0$. 1 Mark
Order = 3 (Highest derivative $\frac{d^3y}{dx^3}$).
Degree = 2 (Power of the highest derivative).
Order = 3, Degree = 2
Q4
2019 Board
00:00
Find the order and degree of $(\frac{d^2y}{dx^2})^2 + (\frac{dy}{dx})^4 = 1$. 1 Mark
Order = 2
Degree = 2
Order = 2, Degree = 2
Q5
2021 Board
00:00
Find the order and degree of $(\frac{d^2y}{dx^2})^4 + (\frac{dy}{dx})^2 = 0$. 1 Mark
Order = 2
Degree = 4
Order = 2, Degree = 4
Q6
2025 Board
00:00
Find the order and degree of $(\frac{d^2y}{dx^2})^3 + \frac{dy}{dx} = 0$. 1 Mark
Order = 2
Degree = 3
Order = 2, Degree = 3