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Hiche
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Homework Statement
Solve the following IVP:
[itex]X' = \begin{pmatrix}2 & -1\\3 & -2\end{pmatrix}X + \begin{pmatrix}0\\t\end{pmatrix}[/itex] with [itex]X(0) = \begin{pmatrix}1\\0\end{pmatrix}[/itex]
Homework Equations
The Attempt at a Solution
The eigenvalue corresponding to [itex]\begin{pmatrix}2 & -1\\3 & -2\end{pmatrix}[/itex] is [itex]\lambda = 0[/itex]. We find that [itex]X_c = c_1\begin{pmatrix}1\\2\end{pmatrix} e^{0t}[/itex]. Now in order to find [itex]X_p[/itex], how exactly is the right way? I took [itex]X_p = \begin{pmatrix}a_1\\b_1\end{pmatrix}t[/itex] and wanted to find [itex]a_1[/itex] and [itex]b_1[/itex]. Right or wrong?