Question:
Write the degree of differential equation \( (y''')^4 + 3(y'') + 3xy + 5y = 0 \)
Write the degree of differential equation \( (y''')^4 + 3(y'') + 3xy + 5y = 0 \)
Show Hint
Degree is the highest power of the highest-order derivative in a polynomial differential equation.
Updated On: Nov 11, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
The degree of a differential equation is the highest power of the highest-order derivative.
Here, the highest-order derivative is \( y''' \), with power 4 in \( (y''')^4 \).
The equation is polynomial in derivatives, so the degree is 4.
Answer: 4.
Here, the highest-order derivative is \( y''' \), with power 4 in \( (y''')^4 \).
The equation is polynomial in derivatives, so the degree is 4.
Answer: 4.
Was this answer helpful?
0
0
Top Questions on Differential Equations
- Find the general solution of differential equation \( ydx + (x - y^2)dy = 0 \).
- UP Board XII - 2025
- Mathematics
- Differential Equations
- Let $ f(x) = x - 1 $ and $ g(x) = e^x $ for $ x \in \mathbb{R} $. If $\frac{dy}{dx} = \left( e^{-2\sqrt{x}} g\left(f\left(f(x)\right)\right) - \frac{y}{\sqrt{x}} \right), \, y(0) = 0,$ then $ y(1) $ is
- JEE Main - 2025
- Mathematics
- Differential Equations
- Solve: \((\tan^{-1}y - x)dy = (1+y^2)dx\).
- UP Board XII - 2025
- Mathematics
- Differential Equations
Let \( y = y(x) \) be the solution of the differential equation \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] such that \( y(0) = \frac{5}{4} \). Then \[ 12 \left( y\left( \frac{\pi}{4} \right) - e^{-2} \right) \] is equal to _____.
- JEE Main - 2025
- Mathematics
- Differential Equations
- If \( x = f(y) \) is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with \( f(0) = 1 \), then \( f\left( \frac{1}{\sqrt{3}} \right) \) is equal to:
- JEE Main - 2025
- Mathematics
- Differential Equations
View More Questions
Questions Asked in Maharashtra Class XII exam
- "If two systems are each in thermal equilibrium with a third system, they are also in thermal equilibrium with each other." This statement refers to :
- Maharashtra Class XII - 2025
- Thermodynamics
- Find the adjoint of the matrix \( \left[ \begin{matrix} 2 & -2 \\ 4 & 3 \end{matrix} \right] \).
- Maharashtra Class XII - 2025
- Matrix Operations
- What is Brewster's law? Derive the formula for Brewster's angle.
- Maharashtra Class XII - 2025
- Wave Optics
- State and prove the law of conservation of angular momentum.
- Maharashtra Class XII - 2025
- Rotational Motion
- If a body cools from 80°C to 50°C at room temperature of 25°C in 30 minutes, find the temperature of the body after 1 hour.
- Maharashtra Class XII - 2025
- Newton's Law of Cooling
View More Questions