Variation of Parameters on a system of Differential Eqs (Simple question)

  • #1
Saladsamurai
3,019
6

Homework Statement


Okay so when solving a system of D.E.s using Variation of Parameters I know that first I find the complementary solution Xc and then do a bunch a of crap after that using the fundamental matrix.

Now I just came across a problem with repeated roots, so I just want to clarify that I am correct in saying that if the complementary solution looks like this:

[tex]X_c=c_1\left(\begin{array}{c}1\\1\end{array}\right)+c_2[\left(\begin{array}{c}1\\1\end{array}\right)t+\left(\begin{array}{c}1\\0\end{array}\right)][/tex]


Then the fundamental matrix looks like this:

[tex]\Phi(t)=\left(\begin{array}{cc}1 & t+1\\ 1 & t\end{array}\right)[/tex]



Just a yes or no will do... (if it's no, I am in trouble!)

Thanks!
 

Answers and Replies

  • #2
Saladsamurai
3,019
6
Anyone? I just want to make sure before I go using this...
 
  • #3
Saladsamurai
3,019
6
Well I thought it was a simple question...
 
  • #4
Saladsamurai
3,019
6
Tina... eat the food!
 
  • #5
Saladsamurai
3,019
6
eat the food!
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
43,021
970

Homework Statement


Okay so when solving a system of D.E.s using Variation of Parameters I know that first I find the complementary solution Xc and then do a bunch a of crap after that using the fundamental matrix.

Now I just came across a problem with repeated roots, so I just want to clarify that I am correct in saying that if the complementary solution looks like this:

[tex]X_c=c_1\left(\begin{array}{c}1\\1\end{array}\right)+c_2[\left(\begin{array}{c}1\\1\end{array}\right)t+\left(\begin{array}{c}1\\0\end{array}\right)][/tex]


Then the fundamental matrix looks like this:

[tex]\Phi(t)=\left(\begin{array}{cc}1 & t+1\\ 1 & t\end{array}\right)[/tex]



Just a yes or no will do... (if it's no, I am in trouble!)

Thanks!

Does it help you to point out that

[tex]\left(\begin{array}{cc}1 & t+1\\ 1 & t\end{array}\right)\left(\begin{array}{c}c_1 \\ c_2\end{array}\right)= \left(\begin{array}{c}c_1+ c_2(t+1) \\ c_1+ c_2t\end{array}\right)[/tex]
 

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