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

djeljenike 2021-09-23 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

Aniqa O'Neill
Answered 2021-09-24 Author has 12661 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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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.
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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
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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.
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