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#### Dhamnekar Winod

##### Active member

- Nov 17, 2018

- 149

$\vec{x'}=\small\begin{pmatrix}1&2\\3&2\end{pmatrix}\vec{x}+t\small\begin{pmatrix}2\\-4\end{pmatrix}$

Now i got the solution to this differential equation system as

$\vec{x}(t)=c_1e^{-t}\small\begin{pmatrix}-1\\1\end{pmatrix}$+$c_2e^{4t}\small\begin{pmatrix}2\\3\end{pmatrix}$+$t\small\begin{pmatrix}3\\\frac{-5}{2}\end{pmatrix}$+$\small\begin{pmatrix}-2.75\\2.875\end{pmatrix}$

Now i converted this differential equation system into ordinary differential equation $y''-3y'-4y+12t-2=0$

I got solution to this DE as $y=C_1e^{-x}+C_2e^{4x}+3t-\frac12$.

Now my question why there is diference in these two solutions?