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anyanavicka [17]
4 years ago
12

Solve the given system of differential equations by systematic elimination

Mathematics
1 answer:
Korolek [52]4 years ago
3 0

\begin{cases}(D^2+2)x-2y=0\\-2x+(D^2+5)y=0\end{cases}

Solve for y(t) in the first ODE:

y=\dfrac{(D^2+2)x}2

Substitute this into the second ODE:

-2x+(D^2+5)\dfrac{(D^2+2)x}2=0

-4x+(D^4+7D^2+10)x=0

(D^4+7D^2+6)x=0

This ODE is linear with characteristic equation

r^4+7r^2+6=(r^2+6)(r^2+1)=0

with roots at r=\pm i\sqrt6 and r=\pm i, so that the characteristic solution x_c(t) is

\boxed{x(t)=C_1\cos(\sqrt6\,t)+C_2\sin(\sqrt6\,t)+C_3\cos t+C_4\sin t}

and from here we can solve for y(t):

y=\dfrac{(D^2+2)x}2

\boxed{y(t)=-2C_1\cos(\sqrt6\,t)-2C_2\sin(\sqrt6\,t)+\dfrac{C_3}2\cos t+\dfrac{C_4}2\sin t}

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Pachacha [2.7K]

Answer:

J = 6/5

Step-by-step explanation:

8−6j=9j−10

Step 1: Simplify both sides of the equation.

8−6j=9j−10

8+−6j=9j+−10

−6j+8=9j−10

Step 2: Subtract 9j from both sides.

−6j+8−9j=9j−10−9j

−15j+8=−10

Step 3: Subtract 8 from both sides.

−15j+8−8=−10−8

−15j=−18

Step 4: Divide both sides by -15.

−\frac{-15j}{-15} = \frac{-18}{-15}

j= \frac{6}{5}

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5 0
3 years ago
Read 2 more answers
Shawn wants to model the number 13,450 using base-ten blocks. how many large cubes, flats, and longs does he need to model the n
enot [183]
1 rod or long is a column of 10 unit cubes.

10 longs placed side by side, form a flat (with dimensions 10×10)

10 flats, placed on top of each other form a large cube, with dimensions 10×10×10 = 1000 cubes.
-------------------------------------------------------------------------------------------------

each small cube (unit cube) represents the number 1.

thus each long represents 10
each flat represents 100

and each large cube represents 1,000


The number 13,450 can be written as

1*10,000+3*1000+4*100+5*10 using the expanded form.

This means that there are 13 large cubes, 4 flats and 5 longs needed to model the number.


Answer: 13 large cubes, 4 flats, 5 longs

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4 years ago
WILL GIVE THE BRAINLEST <br><br>Find the area of the figure​
seropon [69]
I would split it like this so you have:
- A rectangle that's 8 x 10
- A square that's 4 x 4
- A triangle with a base = 2 and a height = 4

Area of rectangle: b * h
8 * 10 = *80*

Area of square: b * h
4 * 4 = *16*

Area of triangle: 1/2 * b * h
(1/2)(2)(4) = *8*

Add up the areas:
80 + 16 + 8

104 is your an answer!
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3 years ago
Graph the function 2 3^sqrt x+2 +4​
Ghella [55]

Answer: b; y intercept between 8 and 4

Step-by-step explanation:

1. a; 2/3

2. b; 3, all real numbers except x=2

3. a; $.75

4. c; intercepting at (-3,-3)

5. b; 5

6. a; starts at 3

7. b; 1975

8. b; y intercept between 8 and 4

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How many leaves on a tree diagram are needed to represent all possible combinations tossing a coin 4 times?
AlekseyPX
1/2 x 1/2 x 1/2 x 1/2 = 1/16

Answer: 16
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