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Mathematics

2 answers:

umka2103 [35]3 years ago

8 0

Answer:

cool among us

Step-by-step explanation:

Have a good day

Usimov [2.4K]3 years ago

4 0

Answer:

Nice among us character :D

Step-by-step explanation:

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

2 years ago

A movie theater sells adult and child tickets.An adult tickets (x=? Costs 8.75 and a child ticket (y) costs 6.50. The expression

Eddi Din [679]

Answer:

Step-by-step explanation:

The question is incomplete as we were not given to numbers of adults and children, neveherless we can assume some figures and plug it into the expression

say number of adult is 15

and number of chidren is 30

In this problem we are going to the values of adults and children tickets into the expression for the total cost and return the answer, which is the total cost of tickets sold

given the expression

8.75 x+ 6.50y

substituting for x and y we have

8.75(15)+ 6.50(30)=

131.25+195=$326.25

The total cost for 15 adults and 30 children is $326.25

5 0

3 years ago

How to solve (3,2) and (5,6) and turn it into 2x-y=4

Zolol [24]

Find the slope between the 2 points and plug inotllto point slope form

5 0

4 years ago

Read 2 more answers

How do you find the standard deviation

jok3333 [9.3K]

In order to find the standard deviation you must find the mean, then subtract the mean to the square, then find the mean of the square, then take the square root of that and you have you're answer.

Hope this helps!

Good luck.

8 0

3 years ago

Prove that root 7 is irrational by the method of contradiction

Alchen [17]

Let assume that $\sqrt7$ is a rational number. Therefore it can be expressed as a fraction $\dfrac{a}{b}$ where $a,b\in\mathbb{Z}$ and $\text{gcd}(a,b)=1$ .