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Examples : Linear Differential Equations Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

FAQs on Examples : Linear Differential Equations Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a linear differential equation?
Ans. A linear differential equation is a type of differential equation in which the dependent variable and its derivatives appear only as linear terms. It can be written in the form: a_n(x)y^n + a_{n-1}(x)y^{n-1} + ... + a_1(x)y' + a_0(x)y = f(x), where y is the dependent variable, y' is its derivative, a_n(x) to a_0(x) are functions of x, and f(x) is a given function.
2. How can I solve a linear differential equation?
Ans. To solve a linear differential equation, one can use various methods such as the method of integrating factors, variation of parameters, or using the Laplace transform. The specific method to use depends on the equation's form and coefficients. By applying these methods, one can find the general solution or a particular solution to the equation.
3. What is the order of a linear differential equation?
Ans. The order of a linear differential equation is determined by the highest derivative that appears in the equation. For example, if the highest derivative is y''', then the equation is of third order. The order of the equation affects the number of initial conditions needed to find a unique solution.
4. Can a linear differential equation have a non-linear function on the right-hand side?
Ans. No, a linear differential equation cannot have a non-linear function on the right-hand side. The right-hand side of a linear differential equation must only contain linear terms involving the dependent variable and its derivatives. If a non-linear function appears, the equation becomes non-linear.
5. Are linear differential equations widely used in real-world applications?
Ans. Yes, linear differential equations have numerous applications in various fields such as physics, engineering, economics, and biology. They are used to model and analyze various phenomena, including population growth, heat transfer, electrical circuits, and chemical reactions. The linearity property allows for easier mathematical analysis and solution techniques, making linear differential equations valuable in practical applications.
204 videos|288 docs|139 tests

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