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Examples : Homogeneous Differential Equations and their Solution Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Examples : Homogeneous Differential Equations and their Solution Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a homogeneous differential equation?
Ans. A homogeneous differential equation is a type of differential equation in which all the terms can be expressed in the form of a function and its derivatives. It does not contain any independent variable.
2. How do you solve a homogeneous differential equation?
Ans. To solve a homogeneous differential equation, we can use the technique of separation of variables or substitute the variables to reduce the equation into a separable form. Then, we can integrate both sides to find the general solution.
3. What is the difference between a homogeneous and non-homogeneous differential equation?
Ans. In a homogeneous differential equation, all the terms can be expressed as a function and its derivatives, while in a non-homogeneous differential equation, there is an additional term that cannot be expressed in this form. The presence of this additional term makes the equation non-homogeneous.
4. Can a homogeneous differential equation have non-zero constant solutions?
Ans. Yes, a homogeneous differential equation can have non-zero constant solutions. These constant solutions are called trivial solutions. However, non-trivial solutions, which are not constant, also exist and can be found by solving the differential equation.
5. Is it possible to have multiple solutions for a homogeneous differential equation?
Ans. Yes, a homogeneous differential equation can have multiple solutions. The general solution of a homogeneous differential equation usually contains a constant of integration, which can take different values. Each value of the constant of integration represents a different solution to the differential equation.
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