The order of the differential equation \(2x^2\,\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0\) is
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
The Correct Option is A
Solution and Explanation
\(2x^2\,\frac{d^2y}{dx^2}-3\frac{dy}{dx}+y=0\)
The highest order derivative present in the given differential equation is \(\frac{d^2y}{dx^2}\).
Therefore, its order is two.
Hence, the correct answer is A . (2)
Top Questions on Differential equations
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
- JEE Advanced - 2025
- Mathematics
- Differential equations
- Solve the differential equation: \[ x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x \]
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- Find the particular solution of the differential equation \( \frac{dy}{dx} - \frac{y}{x} + \csc\left(\frac{y}{x}\right) = 0 \); given that \( y = 0 \), when \( x = 1 \).
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- The integrating factor of the differential equation \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \) is:
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
Concepts Used:
Order and Degree of Differential Equation
The equation that helps us to identify the type and complexity of the differential equation is the order and degree of a differential equation.
The Order of a Differential Equation:
The highest order of the derivative that appears in the differential equation is the order of a differential equation.
The Degree of a Differential Equation:
The highest power of the highest order derivative that appears in a differential equation is the degree of a differential equation. Its degree is always a positive integer.
For examples:
- 7(d4y/dx4)3 + 5(d2y/dx2)4+ 9(dy/dx)8 + 11 = 0 (Degree - 3)
- (dy/dx)2 + (dy/dx) - Cos3x = 0 (Degree - 2)
- (d2y/dx2) + x(dy/dx)3 = 0 (Degree - 1)