Question

Consider the following system of differential equations frac{dx}{dt} + y = 0, frac{dy}{dt} - 2x - 3y = 0. a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form $egin{pmatrix} x \ y end{pmatrix} = C_1 egin{pmatrix} 1 \ y_1 end{pmatrix} e^{lambda_1 t} + C_2 egin{pmatrix} 1 \ y_2 end{pmatrix} e^{lambda_2 t}$ where $C_1$ and $C_2$ are constants. Give the values of $lambda_1$, $y_1$, $lambda_2$ and $y_2$. Enter your values such that $lambda_1 < lambda_2$. $lambda_1 = $ ______ $y_1 = $ ______ $lambda_2 = $ ______ $y_2 = $ b) Find the particular solution, expressed as $x(t)$ and $y(t)$, which satisfies the initial conditions $x(0) = 4$, $y(0) = -5$. $x(t) = $ $y(t) = $ __

          Consider the following system of differential equations
frac{dx}{dt} + y = 0,
frac{dy}{dt} - 2x - 3y = 0.
a)
Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form
$egin{pmatrix} x \ y end{pmatrix} = C_1 egin{pmatrix} 1 \ y_1 end{pmatrix} e^{lambda_1 t} + C_2 egin{pmatrix} 1 \ y_2 end{pmatrix} e^{lambda_2 t}$
where $C_1$ and $C_2$ are constants. Give the values of $lambda_1$, $y_1$, $lambda_2$ and $y_2$. Enter your values such that $lambda_1 < lambda_2$.
$lambda_1 = $ ______    $y_1 = $ ______
$lambda_2 = $ ______    $y_2 = $ ______
b)
Find the particular solution, expressed as $x(t)$ and $y(t)$, which satisfies the initial conditions $x(0) = 4$, $y(0) = -5$.
$x(t) = $ ______
$y(t) = $ ______

$Consider the following system of differential equations fracdxdt + y = 0, fracdydt - 2x - 3y = 0. a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form eginpmatrix x y endpmatrix = C1 eginpmatrix 1 y1 endpmatrix e^lambda1 t + C2 eginpmatrix 1 y2 endpmatrix e^lambda2 t where C1 and C2 are constants. Give the values of lambda1, y1, lambda2 and y2. Enter your values such that lambda1 < lambda2. lambda1 = y1 = lambda2 = y2 = b) Find the particular solution, expressed as x(t) and y(t), which satisfies the initial conditions x(0) = 4, y(0) = -5. x(t) = y(t) =$

Added by Melissa R.

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