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

generals336 2021-09-14 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.
\(\lambda_1=2\Rightarrow\left\{\begin{bmatrix}4 \\3 \\1 \end{bmatrix}\right\},\lambda_2=-2\Rightarrow\left\{\begin{bmatrix}1 \\2 \\0 \end{bmatrix},\begin{bmatrix}2 \\3 \\1 \end{bmatrix}\right\}\)

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Expert Answer

Derrick
Answered 2021-09-15 Author has 15485 answers
y1=4c1e^2t+c2e^-2t+2c3e^-2t
y2=3c1e^2t+2c2e^-2t+3c^-2t
y3=c1e^2t+x3e^-2t
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Relevant Questions

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

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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.
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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

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

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