- #1
bhanesh
- 9
- 0
Friends I have one doubt
Below given equation is linear or non linear
:)
Below given equation is linear or non linear
:)
Mathematically,the equation you wrote is considered a linear ordinary differential equation with non-constant coefficients. It is considered linear if the homogeneous part is linear with respect to the dependent variable (in this case y).bhanesh said:
That's not included in the homogeneous part.bhanesh said:
Linearity refers to the property of a mathematical equation or system that follows the principle of superposition. This means that the overall response of the system is a linear combination of the individual responses to each input.
In differential equations, linearity refers to the property of an equation where the dependent variable and its derivatives appear only in the first degree. This allows for the use of linear operators and techniques to solve the equation.
A linear differential equation is an equation that can be written in the form of a linear combination of the dependent variable, its derivatives, and the independent variable. This means that the equation is linear with respect to the dependent variable and its derivatives.
To determine linearity, you can check if the equation follows the principle of superposition. If the equation is in the form of a linear combination of the dependent variable and its derivatives, it is a linear differential equation. Otherwise, it is non-linear.
Linear differential equations have well-defined properties that make them easier to solve compared to non-linear equations. They also have well-known solutions and can be used to model a wide range of physical systems and phenomena.