The particular solution is: [tex]y_{p(x)}[/tex] = (-1/32) cos(4x) + (1/32) sin(4x)
and the general solution to the nonhomogeneous differential equation is:
[tex]y(x) = y_{c(x)} + y_{p(x)} = c_1 cos(4x) + c_2 sin(4x) - (1/32) cos(4x) + (1/32) sin(4x)[/tex]
where c₁ and c₂ are constants determined by initial conditions.
What is the homogeneous differential equation?
A homogeneous differential equation is a differential equation in which all the terms can be expressed as a function of the dependent variable and its derivatives. In other words, a homogeneous differential equation can be written in the form:
F(x, y, y', y'', ..., yⁿ) = 0
To find a particular solution to the nonhomogeneous differential equation:
yⁿ + 16y = cos(4x) + sin(4x)
we can use the method of undetermined coefficients.
First, we find the complementary solution to the homogeneous differential equation:
yⁿ + 16y = 0
The characteristic equation is:
rⁿ + 16 = 0
which has roots:
r = ±4i
The complementary solution is:
[tex]y_{c(x)} = c_1 cos(4x) + c_2 sin(4x)[/tex]
where c₁ and c₂ are constants determined by initial conditions.
Next, we find a particular solution [tex]y_{p(x)}[/tex] to the nonhomogeneous differential equation using the following steps:
Find the general form of the nonhomogeneous term:
cos(4x) + sin(4x) = A cos(4x) + B sin(4x)
where A and B are constants to be determined.
Find the derivatives of the general form of [tex]y_{p(x)}[/tex]:
[tex]y_{p(x)}[/tex]= A cos(4x) + B sin(4x)
[tex]y'_{p(x)}[/tex]= -4A sin(4x) + 4B cos(4x)
[tex]y''_{p(x)}[/tex] = -16A cos(4x) - 16B sin(4x)
Substitute the general form of [tex]y_{p(x)}[/tex] and its derivatives into the nonhomogeneous differential equation:
(-16A cos(4x) - 16B sin(4x)) + 16(A cos(4x) + B sin(4x)) = cos(4x) + sin(4x)
Simplifying, we get:
(16B - 16A) sin(4x) + (16A + 16B) cos(4x) = cos(4x) + sin(4x)
Since this equation must hold for all values of x, we equate the coefficients of sin(4x) and cos(4x) separately:
16B - 16A = 1
16A + 16B = 1
Solving for A and B, we get:
A = -1/32
B = 1/32
Therefore, the particular solution is: [tex]y_{p(x)}[/tex] = (-1/32) cos(4x) + (1/32) sin(4x)
and the general solution to the nonhomogeneous differential equation is:
[tex]y(x) = y_{c(x)} + y_{p(x)} = c_1 cos(4x) + c_2 sin(4x) - (1/32) cos(4x) + (1/32) sin(4x)[/tex]
where c₁ and c₂ are constants determined by initial conditions.
To learn more about the homogeneous differential equation visit:
https://brainly.com/question/30331454
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Compete question:
Find a particular solution to the non-homogeneous differential equation yⁿ + 16y = cos(4x) + sin(4x)
x² + 2xy ty = 144
(x+y)³= ?
Answer:
t=144x3+432x2y+432xy2+144y3−x2
2xy2
Step-by-step explanation:
Susan Marciano invested part of her $27,000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each investment if her overall net profit was $1,590.
Researchers in plant growth are investigating the proportions of seedlings that sprout under two environmental settings in a lab experiment. Let pˆC represent the sample proportion of seedlings that sprout in garden C, and let pˆH represent the sample proportion of seedlings that sprout in garden H. For random samples of 100 garden C seedlings and 100 garden H seedlings, the sampling distribution of the difference between sample proportions pˆC−pˆH has σpˆC−pˆH≈0.051. Which of the following is the best interpretation of σPˆC−PˆH≈0.051 ?
Answer:
E
Step-by-step explanation:
For all random samples of 100 garden C seedlings and 100 garden H seedlings, the average distance of all possible differences between sample proportions pˆC−pˆH from the mean of the sampling distribution is approximately 0.051.
Which group contains triangles that are similar for brainliest
Answer:
its the second one of course
Step-by-step explanation: plz mark brainliest
Answer:A
Step-by-step explanation:
Because yes
Help Plz
You are playing a game that requires flipping a coin twice. Use a sample space to determine whether flipping heads and then tails are independent events.
Answer:
Yes , it is independent
Step-by-step explanation:
independent
{y=5x-7
y=-2x+7 Solve the system by graphing.
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Answer: Put both equation into desmos and the crossing point will be (2,3) and the graph will be there.
Step-by-step explanation: 5x-7 = -2x+7 y = 5(2) - 7
5x = -2x + 7 + 7. y = 3
5x = -2x + 14
5x + 2x = 14
7x = 14
x = 2
Which problem matches the given inequality? d > 12.75 Chelsea spent $12.75. Chelsea spent about $12.75. Chelsea spent less than $12.75. Chelsea spent more than $12.75.
Answer:
Chelsea spent more than $12.75
Step-by-step explanation:
To solve this problem we should understand the meaning of signs first.
sign (<) → less than
sign (>) → more than
sign (=) → equal to
sign (≤) → Not more than
sign (≥) → At least
If the statement is,
"Chelsea spent more than $12.75"
d > 12.75
Therefore, Chelsea spent more than $12.75 is the correct statement.
Answer:
Chelsea spent more than $12.75.
Step-by-step explanation:
bc ik.
% of 25 shirts is 8 shirts.
Answer:
32% of 25 is 8
Step-by-step explanation:
You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make?
Answer:
3
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
3 x 4 = 12
I NEED THIS RN AS FAST AS POSSIBLE! Your teacher decides to split the class into four equal groups with no more than five students in each group. that represents the number of students in the class.
Encierra todo los números que sean mayores a 18,031 2
no se me alludas a saber cual es
Simplify the mathematical expressions and arrange them in order of their values from least to greatest. ↓ ↓ ↓ ↓
Answer and Step-by-step explanation:
To simplify algebraic expressions, follow the basic rules:
1. Remove brackets or parentheses by multiplying factors;
2. Use exponent rule to remove grouping, if terms have exponents;
3. Add or subtract like terms;
4. Combine constants;
In the expressions above, there only constants and scientific notations, i.e., exponents elevated on a base 10. So, to simplify, we multiply the numbers and add the exponents:
(4.27 x 10⁸)(9.2 x 10⁻⁵) = 39.28 x 10³
(6.96 x 10⁵)(8.43 x 10⁻²) = 58.67 x 10³
[tex]\frac{(7.25.10^{5})(9.36.10^{-7})}{(7.95.10^{-2})(4.13.10^{-3})}=[/tex] 2.07 x 10³
[tex]\frac{(8.32.10^{4})(9.67.10^{1})}{(7.56.10^{11})(5.79.10^{-8})}[/tex] = 1.84 x 10²
[tex]\frac{(1.89.10^{4})(5.92.10^{3})}{(2.74.10^{-2})(4.67.10^{2})}=[/tex] 0.875 x 10⁷
All the exponents are positive, which means, comma "moves" to the right.
The numbers arranged from least to greatest will be
1.84 x 10² < 2.07 x 10³ < 39.28 x 10³ < 58.67 x 10³ < 0.875 x 10⁷
Two rectangles we're used to form the following figure. Which measurement is closest to the area of the shaded region of this figure in square inches
Answer:
44 cm
Step-by-step explanation:
You have to find the area of the bigger square and find the area of the smaller one. (Width x Height). Then subtract the smaller rectangle from the bigher one
9. Which of these was an example of US industrial mobilization for war? (5.1.B) A. Increased factory production of tanks and planes B. Increased farm production of wheat C. Rationing of products, like copper and rubber D. Increased production of automobiles
Answer:
A
Step-by-step explanation:
Tanks are the Backbone of the Military, they are needed to destroy the Axis Powers during WW2, they also used Captured Enemy Tanks for studying and Produce New Tanks to Counter them.
Select the equation of the line of symmetry shown at the graph.
Answer choices:
X=3
Y=3
X=4
X=2
NO ONE IS HELPINNGGGG PLZZZZ 30 PTS +brainliest
Answer:
360
Step-by-step explanation:
all quadrilateral angle sums are 360° no matter how you change it
What is the image of M(11,-4) using the translation (x,y) →x-17, y + 2?
A. M'(-6,-2)
B. M'(6,2)
C. M'(-11,4)
D. M'(-4,11)
Answer:
https://cdn.kutasoftware.com/Worksheets/PreAlg/Reflections%20of%20Shapes.pdf
Step-by-step explanation:
pls search this
Answer:
A. M'(-6,-2)
Step-by-step explanation:
PLS PLS help!
Type an equation of a parabola that is moved down 2 units, stretched vertically by a factor of 3, and moved left 5 units.
9514 1404 393
Answer:
y = 3x^2 +30x +69
Step-by-step explanation:
Transformations work this way:
g(x) = k·f(x) . . . . vertical stretch by a factor of k
g(x) = f(x -h) +k . . . . translation (right, up) by (h, k)
__
So, the translation down 2 units will make the function be ...
f(x) = x^2 ⇒ f1(x) = f(x) -2 = x^2 -2
The vertical stretch by a factor of 3 will make the function be ...
f1(x) = x^2 -2 ⇒ 3·f1(x) = f2(x) = 3(x^2 -2)
The horizontal translation left 5 units will make the function be ...
f2(x) = 3(x^2 -2) ⇒ f2(x +5) = f3(x) = 3((x +5)^2 -2)
The transformed function equation can be written ...
y = 3((x +5)^2 -2) = 3(x^2 +10x +25 -2)
y = 3x^2 +30x +69
__
The attachment shows the original function and the various transformations. Note that the final function is translated down 6 units from the original. That is because the down translation came before the vertical scaling.
Solve the equation w=cx-h for x.
Answer:
That's your answer. Let me know if you need an explanation.
Daniel's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 1 adult ticket and 3 child tickets for a total of $39. The school took in $87 on the
second day by selling 5 adult tickets and 3 child tickets. Find the price of an adult ticket and the
price of a child ticket.
Answer:
Your answer.
Adult ticket = 12
Child ticket = 9
Thank you. And give my answer as Brainlist answer. Follow me for more
Step-by-step explanation:
Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.
Drag and drop the choices into the boxes to correctly complete the table.
corresponding alternate interior alternate exterior none of these
Answer:
From left to right, top to bottom: 1 and 2 are neither, 1 and 2 are neither, 1 and 2 are neither, 1 and 2 are cooresponding angles, 1 and 2 are alterante interior angles.
Answer:
We will go in order.
first-None of them
second-Alternate exterior
third-None of them
forth-Corresponding
and Fifth-Alternate Interior
Step-by-step explanation:
just took test
The length of a rectangle is three times its width.
If the width is represented by x, what is the
perimeter of the rectangle, in terms of x?
Answer:
perimeter:- 8x
Step-by-step explanation:
since,
length= 3(width)
length= 3x
and, perimeter= 2(l + b)
= 2(3x + x)
= 2(4x)
perimeter = 8x
are 7/18 and -21/-56 are equivalent
Answer:
yes they are equivalent. if you simplify -21/-56 by dividing it by 3 you will get -7/-21 which equals to 7/21
Compare the number of friends at the beginning of a month and at the end of that month if it decreased by 60 and increased by 80
Answer:
plus 20 or positive
Step-by-step explanation:
-60+80= 20
positive
There are 6 dogs and 12 cats in the backyard. Write the ratio of cats to total animals In 3 ways, in simplest form.
Step-by-step explanation:
12:18
12 to 18
12/18 = 2/3
is it possible to have triangle with 3 cm 6 cm and 7 cm sides if yes then
Answer:
No
Step-by-step explanation:
Step-by-step explanation:
Yes it is possible to have a triangle with 3 cm, 6 cm and 7 cm sides because in order to form a triangle the length of two sides of a triangle should exceed the third side as shown below :
3 + 6 > 7
9 > 7( True) ✔
6 + 7 > 3
13 > 3 ( True) ✔
7 + 3 > 6
10 > 6 ( True) ✔
Hope it will help :)
whats 3squared correct to 5 decimal places
Answer:
9.0000
Step-by-step explanation:
3 squared = 3*3 = 9
9 to 5 decimal places = 9.0000
pls mark as brainliest
11. Justin needs to rent a car to go on vacation. EnvoCar charges $65 and $0.10 per mile. FreedomRide charges $80 and $0.05 per mile.
_________________________
a. How much more does Freedom Ride charge for driving m miles than EnvoCar?
_________________________
b. If Justin’s round-trip distance is 250 miles, which car rental company should he rent from? Explain.
[tex]envo \: car = 65 + 0.10(m)[/tex]
[tex]freedom \: ride = 80 + 0.05(m)[/tex]
//
I honestly don't know how to do a)
//
[tex]envo \: car = 65 + 0.10(250) = 90.00[/tex]
[tex]freedom \: ride = 80 + 0.05(250) = 92.50[/tex]
He should rent from Envo Car because it would be cheaper.
The means and mean absolute deviations of the amount of rain that fell each day in a local city, last week and this week, are shown below. Means and Mean Absolute Deviations of Rainfall Last Week and This Week Last Week This Week Mean 3.5 in. 2.7 in. Mean Absolute Deviation 1.2 in. 0.5 in. Which expression compares the difference of the two means to this week's mean absolute deviation?
Answer:
0.8 / 0.5
Step-by-step explanation:
Given :
Deviations of Rainfall :
______Last Week ____ This Week
Mean___ 3.5 in. ________2.7 in
MAD ___ 1.2 in _________ 0.5 in
Mean difference = 3.5 in - 2.7 in = 0.8 in
This week's mean absolute deviation = 0.5 in
Mean difference / this week's mean absolute deviation
= 0.8 / 0.5
Answer:
0.8 / 0.5
Step-by-step explanation:
Find the value of x
x°
66°
117°
Answer:
x = 51 degrees
Step-by-step explanation:
Keep in mind, the angles of a triangle add up to 180 degrees.
A flat line also equals 180 degrees.
First, we should find the lower left angle. We know that 117 plus that angle is going to be 180, since it's a flat line.
180 - 117 = 63
Now, we just need to find angle x. (All 3 of our angles should add up to 180, knowing this, we can put it in an equation)
63 + 66 + x = 180
Then, you solve for x:
(63+66) + x = 180
129 + x = 180
-129 -129
x = 51
Hope this helps :)