- #1
Benny
- 584
- 0
Hi, I'm having trouble finding the particular solution of the following system.
[tex]
\left[ {\begin{array}{*{20}c}
{\mathop x\limits^ \bullet } \\
{\mathop y\limits^ \bullet } \\
\end{array}} \right] = \left[ {\begin{array}{*{20}c}
1 & { - 1} \\
{ - 1} & 1 \\
\end{array}} \right]\left[ {\begin{array}{*{20}c}
x \\
y \\
\end{array}} \right] + \left[ {\begin{array}{*{20}c}
2 \\
{ - 5} \\
\end{array}} \right]
[/tex]
I found the complimentary function, it had some sines and cosines in it but I don't think that matters in terms of finding the particular solution. The independent variable t isn't present anywhere in the equation so I don't need to do any differentiation. If I set x' = y' = 0 (the prime denotes differentiation wrt t) then I end up with an 'inconsistent' set of equations, namely, x - y = 2 and x - y = 5. Can someone tell me how I can find the particular solution? Thanks.
[tex]
\left[ {\begin{array}{*{20}c}
{\mathop x\limits^ \bullet } \\
{\mathop y\limits^ \bullet } \\
\end{array}} \right] = \left[ {\begin{array}{*{20}c}
1 & { - 1} \\
{ - 1} & 1 \\
\end{array}} \right]\left[ {\begin{array}{*{20}c}
x \\
y \\
\end{array}} \right] + \left[ {\begin{array}{*{20}c}
2 \\
{ - 5} \\
\end{array}} \right]
[/tex]
I found the complimentary function, it had some sines and cosines in it but I don't think that matters in terms of finding the particular solution. The independent variable t isn't present anywhere in the equation so I don't need to do any differentiation. If I set x' = y' = 0 (the prime denotes differentiation wrt t) then I end up with an 'inconsistent' set of equations, namely, x - y = 2 and x - y = 5. Can someone tell me how I can find the particular solution? Thanks.