- #1

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- 87

If I have been given a system of inhomogeneous linear ODEs,

$$

\vec{x'} =

\begin{bmatrix}

4 & -1 \\

5 & -2 \\

\end{bmatrix}

\vec{x}

+

\begin{bmatrix}

18e^{2t} \\

30e^{2t}\\

\end{bmatrix}

$$

I have found its particular solution to be:

$$

1/4

\begin{bmatrix}

-31e^{2t} - 25e^{6t} \\

85e^{2t} - 25e^{6t} \\

\end{bmatrix}

$$

But this answer doesn't match with the answer given in the book. Can someone tell me how to check if this solutions works by writing some code in Mathematica? I know, I can use DSolve for solving them, but I'm asking a reverse of that.

Please guide me step by step, I'm new to Mathematica and I don't have any background in programming.

$$

\vec{x'} =

\begin{bmatrix}

4 & -1 \\

5 & -2 \\

\end{bmatrix}

\vec{x}

+

\begin{bmatrix}

18e^{2t} \\

30e^{2t}\\

\end{bmatrix}

$$

I have found its particular solution to be:

$$

1/4

\begin{bmatrix}

-31e^{2t} - 25e^{6t} \\

85e^{2t} - 25e^{6t} \\

\end{bmatrix}

$$

But this answer doesn't match with the answer given in the book. Can someone tell me how to check if this solutions works by writing some code in Mathematica? I know, I can use DSolve for solving them, but I'm asking a reverse of that.

Please guide me step by step, I'm new to Mathematica and I don't have any background in programming.

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