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ch2kb0x
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Homework Statement
(x + 2y) dy/dx = 1, y(0) = 1
Homework Equations
The Attempt at a Solution
Problem is, I can't separate it. This might be a homogenous type? If so, how would I make it into the g(y/x) form.
Thank you.
ch2kb0x said:Problem is, I can't separate it. This might be a homogenous type? If so, how would I make it into the g(y/x) form.
Thank you.
You can write the equation as dy/dx = 1/(x + 2y), where the right side is a function of x and y. I'm just offering a suggested approach based on your first post. It may or may not work.ch2kb0x said:Okay, so since you said y = ux, I am thinking that this is a homogenous equation...
However, if it is a homogeneous equation, before we can plug in y = ux, aren't we suppose to first have the equation in the form of dy/dx = f(x,y), where there exists a function such that f(x,y) is expressed g(y/x).
Then, AFTEr we can do the y=ux thing. correct me if I am wrong.
Mark44 said:You can write the equation as dy/dx = 1/(x + 2y), where the right side is a function of x and y. I'm just offering a suggested approach based on your first post. It may or may not work.
A separable differential equation is a type of differential equation where the dependent variable and independent variable can be separated on opposite sides of the equation. This allows for the equation to be solved by integrating both sides separately.
To solve a separable differential equation, you first need to separate the variables on opposite sides of the equation. Then you can integrate both sides separately and solve for the constant of integration. Finally, you can solve for the dependent variable to get the final solution.
Separable differential equations are commonly used in physics, engineering, and other sciences to model real-world phenomena. They can also be used in economics and finance to model growth and decay processes.
The main difference between a separable and non-separable differential equation is that the dependent and independent variables cannot be separated in a non-separable equation. This means that the equation cannot be solved by simply integrating both sides, and other techniques must be used.
While separable differential equations are useful in many applications, they do have some limitations. They can only be used to solve first-order differential equations, and they may not always provide an exact solution. In some cases, numerical methods may need to be used instead.