The problem involves finding a particular solution \( Y_p \) for the differential equation \( 4y'' + 4y' + y = 3xe^x \) using the method of flexible guessing.
The discussion includes various attempts at guessing the form of the particular solution, with some participants questioning the validity of their assumptions. There is no clear consensus, but suggestions for alternative forms have been provided, indicating a productive exploration of the problem.
Participants are navigating the complexities of the method of flexible guessing and are considering different forms for the particular solution based on the equation's structure.
I don't know what you mean by "my A depended on x." A is a constant, so is not dependent on any variable.mike1967 said:Homework Statement
Find a particular solution Yp of the given equation. Primes denote deriviate with respect to x
(method of flexible guess)
Homework Equations
4y''+4y'+y=3xe^x
The Attempt at a Solution
when I used y=Ae^x as guess my A depended on x
Why don't you try yp = Aex + Bxex?mike1967 said:So y=Axe^x gave me 12A+9Ax=3x
12A=0
9Ax=3x
does not work,
Before I go on to trying y=Ax^2e^x am I doing this right?
mike1967 said:Yp=3/9xe^x-4/9e^x right?
This is something you should get in the habit of checking for yourself. You've already done all the hard work. If 4yp'' + 4y' + yp [itex]\equiv[/itex] 3xex, then your solution is correct.mike1967 said:Yp=3/9xe^x-4/9e^x right?