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

Isa Trevino 2021-06-15 Answered

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

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Expert Answer

opsadnojD
Answered 2021-06-16 Author has 18821 answers
\(\displaystyle{y}{1}={c}{1}{e}^{{-{{t}}}}+{c}{2}{e}^{{2}}{t}\)
\(\displaystyle{y}{2}={c}{1}{e}^{{-{{t}}}}-{c}{2}{e}^{{2}}{t}\)
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Relevant Questions

asked 2021-06-17

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

asked 2021-05-01

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

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

\(\lambda1=3\Rightarrow \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}\)

\(\lambda2=0\Rightarrow \begin{bmatrix} 1 \\ 5 \\ 1 \end{bmatrix}\begin{bmatrix}2 \\ 1 \\ 4 \end{bmatrix}\)

asked 2021-09-23
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.
\(\displaystyleλ{1}=-{1}\to{\left\lbrace\begin{array}{cc} {1}&{1}\end{array}\right\rbrace},λ{2}={2}\to{\left\lbrace\begin{array}{cc} {1}&-{1}\end{array}\right\rbrace}\)
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.
\(\displaystyleλ{1}={1}\to{\left\lbrace\begin{array}{cc} {2}&{1}\end{array}\right\rbrace},λ{2}={3}\to{\left\lbrace\begin{array}{cc} {3}&{1}\end{array}\right\rbrace}\)
asked 2021-09-14

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

asked 2021-05-12

Form (a) the coefficient matrix and (b) the augmented matrix for the system of linear equations. \(\begin{cases} 7 x-5 y=11\\ x-y=-5 \end{cases}\)

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