Differential Equations Method of Flexible guessing

[mike1967]

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
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?

 

[Mark44]

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

I don't know what you mean by "my A depended on x." A is a constant, so is not dependent on any variable.

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?

Why don't you try y_p = Ae^x + Bxe^x?

 

[mike1967]

Yp=3/9xe^x-4/9e^x right?

 

[Dick]

Yp=3/9xe^x-4/9e^x right?

Right.

 

[Mark44]

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 4y_p'' + 4y' + y_p $\equiv$ 3xe^x, then your solution is correct.