\(\displaystyle{y}{2}={c}{1}{e}^{{-{{t}}}}-{c}{2}{e}^{{2}}{t}\)

asked 2021-09-20

The coefficient matrix for a system of linear differential equations of the form y′=Ay has the given eigenvalues and eigenspace bases. Find the general solution for the system.

\(\displaystyleλ{1}={1}\to{\left\lbrace\begin{array}{cc} {2}&{1}\end{array}\right\rbrace},λ{2}={3}\to{\left\lbrace\begin{array}{cc} {3}&{1}\end{array}\right\rbrace}\)

\(\displaystyleλ{1}={1}\to{\left\lbrace\begin{array}{cc} {2}&{1}\end{array}\right\rbrace},λ{2}={3}\to{\left\lbrace\begin{array}{cc} {3}&{1}\end{array}\right\rbrace}\)

asked 2021-09-14

\(\lambda_1=2\Rightarrow\left\{\begin{bmatrix}4 \\3 \\1 \end{bmatrix}\right\},\lambda_2=-2\Rightarrow\left\{\begin{bmatrix}1 \\2 \\0 \end{bmatrix},\begin{bmatrix}2 \\3 \\1 \end{bmatrix}\right\}\)

asked 2021-06-15

\(\displaystyleλ{1}=-{1}\to{\left\lbrace\begin{array}{cc} {1}&{1}\end{array}\right\rbrace},λ{2}={2}\to{\left\lbrace\begin{array}{cc} {1}&-{1}\end{array}\right\rbrace}\)

asked 2021-06-17

\(\displaystyleλ_{1}={1}\Rightarrow \left\{\left[\begin{array}{c}2\\ -1\end{array}\right]\right\},λ_{2}={3}\Rightarrow \left\{\left[\begin{array}{c}3\\ 1\end{array}\right]\right\}\)

asked 2021-05-01

\(\lambda1=2\Rightarrow\{[4,3,1]\},\ \lambda2=-2\Rightarrow \{[1,2,0],[2,3,1]\}\)

asked 2021-08-09

The coefficient matrix for a system of linear differential equations of the form \(\displaystyle{y}^{{1}}={A}_{{y}}\) has the given eigenvalues and eigenspace bases. Find the general solution for the system.

asked 2021-02-21

\(\left[\lambda_{1}=-1\Rightarrow\left\{\begin{bmatrix}1 0 3 \end{bmatrix}\right\},\lambda_{2}=3i\Rightarrow\left\{\begin{bmatrix}2-i 1+i 7i \end{bmatrix}\right\},\lambda_3=-3i\Rightarrow\left\{\begin{bmatrix}2+i 1-i -7i \end{bmatrix}\right\}\right]\)