The problem involves solving the differential equation xy' - 4y = x4ex, which is situated within the context of integration techniques and the use of integrating factors.
The discussion is ongoing, with participants exploring different interpretations and approaches to the problem. Some guidance has been provided regarding the use of integrating factors and the product rule, but no consensus has been reached on the next steps.
There is a noted difficulty in expressing the left side of the equation as a derivative, which is central to the discussion. The participants are also navigating the implications of using integrating factors in their attempts.
The whole purpose of finding an integrating factor is so that you can rewrite the left side as the derivative of something.BarackObama said:Homework Statement
xy' - 4y = x4ex
Homework Equations
The Attempt at a Solution
y' - 4x-1y = x3ex
x-4y' - 4x-5y = x-1ex
I'm not sure what to do next, I can't express the LS as a derivative
The whole point of an "integrating factor", u, is that the left side becomes (uy)'. You found x^{-4} as integrating factor so the left side must be (x^{-4}y)'.BarackObama said:Homework Statement
xy' - 4y = x4ex
Homework Equations
The Attempt at a Solution
y' - 4x-1y = x3ex
x-4y' - 4x-5y = x-1ex
I'm not sure what to do next, I can't express the LS as a derivative