- #1
WMDhamnekar
MHB
- 378
- 28
Hello,
$\vec{x'}=\small\begin{pmatrix}1&2\\3&2\end{pmatrix}\vec{x}+t\small\begin{pmatrix}2\\-4\end{pmatrix}$
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?
$\vec{x'}=\small\begin{pmatrix}1&2\\3&2\end{pmatrix}\vec{x}+t\small\begin{pmatrix}2\\-4\end{pmatrix}$
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?