The problem involves a differential equation of the form (x + 2y) dy/dx = 1, with an initial condition y(0) = 1. Participants are exploring whether it can be classified as a homogeneous equation and discussing the appropriate methods for separation or substitution.
The discussion is ongoing, with participants offering various approaches and questioning the assumptions about the equation's form. There is no explicit consensus, but suggestions for potential methods have been provided, including the substitution and rewriting the equation.
Participants note the challenge of separating the equation and the requirement for it to be expressed in a specific form before applying certain methods. There is also mention of the original problem being taken directly from a textbook.
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.