PLZZ ANSWERPLZ PZLZZZZ

Simora [160]

From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

$3r^2-6r+6=0\iff r^2-2r+2=0$

which has roots at $r=1\pm i$ . This admits the two fundamental solutions

$y_1=e^x\cos x$
$y_2=e^x\sin x$

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

and so

$u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx$
$u_1=\dfrac13\ln|\cos x|$

$u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx$
$u_2=\dfrac13x$

Therefore the particular solution is

$y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

so that the general solution to the ODE is

$y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

7 0

2 years ago

The camp will pay you $48.23 each day for 8 weeks. If you work 5 days each wee , how much money will you make this summer ?

AlekseyPX

Answer:$1,929.20

Step-by-step explanation:First off, I noted that the answers are pretty far apart so I rounded up to $50 to make it simpler (you should only do this if the answers are pretty far apart from one another.)

$50 per day × 5 days per week × 8 weeks = $2,000. Closest answr (because I rounded) is $1,929.20.

3 0

3 years ago

Read 2 more answers

What is 5x^2y^-3 simplified?

xxTIMURxx [149]

Answer:

(5x^2)/(y^3)

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Knight and Haslam (2010) found that office workers who had some input into the design of their office space were more productive

sleet_krkn [62]

Answer:

1. Option A

2. Option A

Step-by-step explanation:

1.

The independent variable is the one which affects the other variable. Here two variables "design of office space" and "control by managers" control the Productivity and well-being of the workers.

Hence, the independent variable is Control of the office manager

Option A

2. The dependent variable is the one which gets affected by the independent variable and in this case it is the Productivity and well-being of the workers.

Option A

5 0

2 years ago

Zack plans to borrow $7,300 to buy a car.

Neko [114]

I believe the second one, double check

4 0

2 years ago