- #1
Unassuming
- 167
- 0
Consider, x' = x + 3y^3
y' = -3y
I am trying to use the fundamental matrix, F(t), and 3y^3 as my g(t) in order to plug into the variation of parameters formula...
Xp = F(t) * \integral{ F(t)^-1 * g(t) } ,
Am I going about this the wrong way?
I am trying to get something in a form that I recognize, like
[tex] X' = \begin{pmatrix}1 & 0 \\ 0 & -3\end{pmatrix}
\begin{pmatrix}C_1 \\ C_2\end{pmatrix}
+ \begin{pmatrix} 3y^3 \\ 0 \end{pmatrix}
[/tex]
Can I make that work?
y' = -3y
I am trying to use the fundamental matrix, F(t), and 3y^3 as my g(t) in order to plug into the variation of parameters formula...
Xp = F(t) * \integral{ F(t)^-1 * g(t) } ,
Am I going about this the wrong way?
I am trying to get something in a form that I recognize, like
[tex] X' = \begin{pmatrix}1 & 0 \\ 0 & -3\end{pmatrix}
\begin{pmatrix}C_1 \\ C_2\end{pmatrix}
+ \begin{pmatrix} 3y^3 \\ 0 \end{pmatrix}
[/tex]
Can I make that work?