Differential equations: Homogeneous Linear Equations

In summary, the conversation discusses a video on YouTube about solving homogeneous linear equations in the case of differential equations. The speaker mentions that there will be more videos posted daily and provides some tips for improving the presentation, such as using a white board, improving lighting and sound, and adding more explanation in the videos.
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  • #2
mysolutionshrc said:
Differential equations Homogeneous Linear Equations case 1 +example - YouTube

There are more on my channel and will be posting more daily.

I'm afraid you need to improve you method of presentation.

1. Get a white board. Your text is almost unreadable (too small), the lighting is wrong, it should be in front of you not behind, you are blocking the view of what you are writing with your hand/arm.

2. Greater sound level needed

3. Review the material in the video, there is insufficient explanation of why you are doing what you do.

CB
 

Related to Differential equations: Homogeneous Linear Equations

1. What is a homogeneous linear equation?

A homogeneous linear equation is a differential equation in which all the terms can be expressed as a linear combination of the dependent variable and its derivatives. In other words, the equation is homogeneous because all the terms have the same degree of the dependent variable.

2. What is the general form of a homogeneous linear equation?

The general form of a homogeneous linear equation is y'(x) + p(x)y(x) = 0, where p(x) is a function of x and y(x) is the dependent variable.

3. How do you solve a homogeneous linear equation?

To solve a homogeneous linear equation, you can use the method of separation of variables, where you separate the variables on each side of the equation and then integrate both sides. You can also use the method of integrating factors, where you multiply both sides of the equation by an integrating factor to make it easier to solve.

4. What is the role of initial conditions in solving a homogeneous linear equation?

Initial conditions are necessary to solve a homogeneous linear equation because they provide specific values for the dependent variable and its derivatives at a given point. These values can be used to determine the constants of integration and obtain a particular solution to the differential equation.

5. How are homogeneous linear equations used in real-world applications?

Homogeneous linear equations are used in various fields of science and engineering to model systems where the rate of change of a variable is directly proportional to the variable itself. This includes applications in physics, chemistry, biology, economics, and more.

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