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Reducible to Homogeneous Differential Equation Video Lecture | Mathematics for Competitive Exams
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FAQs on Reducible to Homogeneous Differential Equation Video Lecture - Mathematics for Competitive Exams
| 1. What is a reducible homogeneous differential equation? |  |
Ans. A reducible homogeneous differential equation is a differential equation in which the dependent variable and its derivatives can be expressed as a function of a single variable. It can be reduced to a simpler form by using a suitable substitution.
| 2. How do you determine if a differential equation is reducible to a homogeneous form? | |
Ans. To determine if a differential equation is reducible to a homogeneous form, we can substitute the dependent variable as a product of a function of one variable and a constant. If the resulting equation can be written solely in terms of the function of one variable, then it is reducible to a homogeneous form.
| 3. What is the importance of reducible homogeneous differential equations in IIT JAM Mathematics exam? | |
Ans. Reducible homogeneous differential equations are important in the IIT JAM Mathematics exam as they often appear in various application problems. Being able to identify and solve these types of equations is crucial for success in the exam.
| 4. Can you provide an example of a reducible homogeneous differential equation? | |
Ans. Sure! One example of a reducible homogeneous differential equation is:
xy' - y = x^2
This equation can be reduced to a homogeneous form by substituting y = vx:
x(dx/dt) - vx = x^2
This equation can then be simplified and solved using appropriate techniques.
| 5. What are some common techniques used to solve reducible homogeneous differential equations? | |
Ans. There are several techniques that can be used to solve reducible homogeneous differential equations, including separation of variables, substitution, and integrating factors. These techniques involve manipulating the equation to isolate the dependent variable and then integrating to find the solution. It is important to carefully choose the appropriate technique based on the specific form of the equation.
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Nov 22, 2024 Last updated |
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