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First Order First Degree Differential Equation -3 Video Lecture | Basic Physics for IIT JAM
FAQs on First Order First Degree Differential Equation -3 Video Lecture - Basic Physics for IIT JAM
| 1. What is a first order first degree differential equation? |  |
Ans.A first order first degree differential equation is an equation involving a function and its first derivative, where the highest derivative is of the first order and the equation is linear in the unknown function and its derivative. It can generally be expressed in the form \( \frac{dy}{dx} + P(x)y = Q(x) \).
| 2. How do you solve a first order first degree differential equation? | |
Ans.To solve a first order first degree differential equation, one common method is to use an integrating factor. The integrating factor is typically \( e^{\int P(x)dx} \). Multiply the entire differential equation by this factor, which allows you to express the left side as the derivative of a product, making it easier to integrate both sides.
| 3. What is the significance of the integrating factor in solving these equations? | |
Ans.The integrating factor transforms the differential equation into a form that can be easily integrated. It allows us to combine the terms of the equation into one single derivative, simplifying the process of finding a solution. The solution can then be obtained by integrating both sides of the modified equation.
| 4. Can first order first degree differential equations have unique solutions? | |
Ans.Yes, first order first degree differential equations can have unique solutions under certain conditions. According to the existence and uniqueness theorem, if \( P(x) \) and \( Q(x) \) are continuous functions on an interval, then there exists a unique solution that passes through a given point within that interval.
| 5. What are some applications of first order first degree differential equations? | |
Ans.First order first degree differential equations are widely used in various fields such as physics, engineering, and economics. They can model population growth, radioactive decay, and cooling laws, among other phenomena, making them essential tools in both theoretical and applied sciences.
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Sep 29, 2025
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