Differential Calculus variaton of parameters question

[Ortix]

Homework Statement

The equation that has to be solved:
y'' - y' - 2y = 2e^(-t)


The problem I am having is that I don't understand why they equatate that part with the derivatives of the u parameters to 0. (see image)

Here they first find the characteristic equation and write down the general solution. They then replace the constants with the parameter "u" and take the derivate.

As you can see, they just say that the derivate part of the u parameter is equal to 0. But why? How? Where did that come from? I can't find it anywhere in my book.

It's probably a facepalm answer but I would really appreciate it

 

[jedishrfu]

Isnt the derivative of a constant zero?

 

[Ortix]

yes but for some reason in the examples and solutions they even take the second derivative of u and they leave it in the equation. It's just that those 2 "parts" are equal to 0 for some reason that is unbeknownst to me and my buds here in the library..

 

[jedishrfu]

they may be showing you generalized steps that you should keep in mind for the real world and then reducing them since the u1(t)=constant hence u1'=0 and u1''=0 ...

 

[Ortix]

NEvermind the solution can be found here:
http://math.stackexchange.com/quest...rential-equation-with-variation-of-parameters