# Trying to use variation of parameters

1. Dec 8, 2008

### Unassuming

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) } ,

I am trying to get something in a form that I recognize, like

$$X' = \begin{pmatrix}1 & 0 \\ 0 & -3\end{pmatrix} \begin{pmatrix}C_1 \\ C_2\end{pmatrix} + \begin{pmatrix} 3y^3 \\ 0 \end{pmatrix}$$

Can I make that work?

2. Dec 9, 2008

### Defennder

Um, what does variation of parameters got to do with this one? Your system of DE isn't linear to begin with; look at the DE for x'