Question:
The order of differential equation of all circles of given radius $'a'$ is _____
The order of differential equation of all circles of given radius $'a'$ is _____
Updated On: Apr 14, 2024
- 4
- 2
- 1
- 3
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Let the centre of circle be $( h , k )$ and radius $a$, then its equation will be
$(x-h)^{2}+(y-k)^{2}=a^{2}$
Since, there are two parameters $h$ and $k .$ So, the differential equation is of order 2
$(x-h)^{2}+(y-k)^{2}=a^{2}$
Since, there are two parameters $h$ and $k .$ So, the differential equation is of order 2
Was this answer helpful?
0
0
Top Questions on Order and Degree of Differential Equation
- The degree of the differential equation
\(1+(\frac{dy}{dx})^2+(\frac{d^2y}{dx^2})^2= \sqrt[3]{\frac{d^2y}{dx^2}+1}\) is- KCET - 2023
- Mathematics
- Order and Degree of Differential Equation
- Domain of \(cos^{-1} [x]\), where \([. ]\) denotes a greatest integer function
- KCET - 2022
- Mathematics
- Order and Degree of Differential Equation
- The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_1y = (c_2 +c_3 )e^{x+c_4}$ is
- KCET - 2020
- Mathematics
- Order and Degree of Differential Equation
- The order and degree of the differential equation $y=x\frac{dy}{dx}+\frac{2}{\frac{dy}{dx}}$ is
- KCET - 2014
- Mathematics
- Order and Degree of Differential Equation
- Solution of $e^\frac {dy}{dx} = x$ when $x = 1$ and $y = 0$ is
- KCET - 2012
- Mathematics
- Order and Degree of Differential Equation
View More Questions
Questions Asked in KCET exam
- Ten identical cells each emf 2V and internal resistance 1Ω are connected in series with two cells wrongly connected. A resistor of 10Ω is connected to the combination. What is the current through the resistor?
- KCET - 2023
- Cells in Series and in Parallel
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
View More Questions
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)