kuCAu
2021-06-26
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Willie

Answered 2021-06-27
Author has **95** answers

We are given:

Subtract 3 from both sides:

Subtract 2y from both sides:

Divide both sides by 3:

asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2021-02-02

If a system of linear equations has infinitely many solutions, then the system is called _____. If a system of linear equations has no solution, then the system is called _____.

asked 2022-02-25

If we were given two points on a linear equation $({x}_{1},{y}_{1}),({x}_{2},{y}_{2})$ , it is quite easy to find the slope and use substitution to find the slope intercept form $y=mx+b$ , to graph it.

Is it possible to solve for b strictly in terms of$x}_{1},{y}_{1},{x}_{2},{y}_{2$ ?

Is it possible to solve for b strictly in terms of

asked 2021-02-08

Solve (1,2)

asked 2022-05-16

Consider the following linear system of differential equations:

$\{\begin{array}{l}\dot{x}=-4y\\ \dot{y}=x\end{array}$

where $x(t)$ and $y(t)$ are unknown real functions.

One can simply verify that the general solution is

$\left(\begin{array}{c}x(t)\\ y(t)\end{array}\right)={c}_{1}\left(\begin{array}{c}\mathrm{cos}(2t)\\ \frac{1}{2}\mathrm{sin}(2t)\end{array}\right)+{c}_{2}\left(\begin{array}{c}-2\mathrm{sin}(2t)\\ \mathrm{cos}(2t)\end{array}\right)$

where ${c}_{1}$ and ${c}_{2}$ are real parameters.

Question: Which is the exponential form of this expression? It should by something like

$\left(\begin{array}{c}x(t)\\ y(t)\end{array}\right)={k}_{1}{e}^{i2t}\left(\begin{array}{c}{P}_{11}\\ {P}_{21}\end{array}\right)+{k}_{2}{e}^{-i2t}\left(\begin{array}{c}{P}_{12}\\ {P}_{22}\end{array}\right)$

where ${k}_{1}$ and ${k}_{2}$ should (?) be complex parameters.

$\{\begin{array}{l}\dot{x}=-4y\\ \dot{y}=x\end{array}$

where $x(t)$ and $y(t)$ are unknown real functions.

One can simply verify that the general solution is

$\left(\begin{array}{c}x(t)\\ y(t)\end{array}\right)={c}_{1}\left(\begin{array}{c}\mathrm{cos}(2t)\\ \frac{1}{2}\mathrm{sin}(2t)\end{array}\right)+{c}_{2}\left(\begin{array}{c}-2\mathrm{sin}(2t)\\ \mathrm{cos}(2t)\end{array}\right)$

where ${c}_{1}$ and ${c}_{2}$ are real parameters.

Question: Which is the exponential form of this expression? It should by something like

$\left(\begin{array}{c}x(t)\\ y(t)\end{array}\right)={k}_{1}{e}^{i2t}\left(\begin{array}{c}{P}_{11}\\ {P}_{21}\end{array}\right)+{k}_{2}{e}^{-i2t}\left(\begin{array}{c}{P}_{12}\\ {P}_{22}\end{array}\right)$

where ${k}_{1}$ and ${k}_{2}$ should (?) be complex parameters.

asked 2021-02-01

Write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3

asked 2022-02-17

How to solve the system of linear differential equation of the form

${x}^{\prime}=Ax+b$

I can solve the homogeneous form by finding the eigenvalues and respective eigenvectors, but how to find the particular solution part. Also is there any limitation from getting eigenvalues positive, negative or complex. Any other different method involving matrix algebra is also welcome.

I can solve the homogeneous form by finding the eigenvalues and respective eigenvectors, but how to find the particular solution part. Also is there any limitation from getting eigenvalues positive, negative or complex. Any other different method involving matrix algebra is also welcome.