Solve the differential equation y" + 3y' + 2y = P1 where, y" = d2y/dx2, y' = dy/dx, P1 = P1(x)) and the initial conditions are y(0) = 0, y'(0) = 0. The input function is given by P1() = { 0, < 0 1, 0 ≤ ≤ 1 0, > 1

Answer:

[tex]y(x) = 0[/tex]

Step-by-step explanation:

Let P(1) = 0, the differential equation becomes:

y" + 3y' + 2y = 0

Also let y' = my and y'' = m²y

Substitute

m²y+3my+2y = 0

(m²+3m+2)y = 0

The auxiliary equation is expressed as:

m²+3m+2 = 0

Factorize

m²+2m+m+2 = 0

m(m+2)+1(m+2) = 0

(m+1)(m+2) = 0

m+1 = 0 and m+2 = 0

m₁ = -1 and m₂ = -2

Since the value of m is real and distinct, the solution to the differential equation will be expressed as:

[tex]y = C_1e^{m_1x}+C_2e^{m_2x}\\[/tex]

[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\[/tex]

Given the initial condition y(0) = 0

[tex]y(0) = C_1e^{-0}+C_2e^{-2(0)}\\0 = C_1+C_2\\C_1+C_2 = 0 ................. 1[/tex]

If y'(0) = 0

[tex]y'(x) = -C_1e^{-x}-2C_2e^{-2x}\\y'(0) = -C_1e^{-0}-2C_2e^{-2(0)}\\0 = -C_1-2C_2\\C_1-2C_2 = 0...................... 2[/tex]

Solve eqn 1 and 2 simultaneously

From 1:

C₁ = -C₂ .......... 3

Substitute equation 3 into 2:

-C₂-2C₂ = 0

-3C₂ = 0

C₂ = 0

Substitute the constant into the differential equation.

[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\\\y(x) = 0[/tex]

3. In the month of August, a car dealership sold a total of 72
cars and trucks. The dealership reported that for every 4
passenger cars sold, there were 2 trucks sold. How many of
each type of vehicle were sold in the month of August?

PLEASE HELP MEEEEEEEEEEEEE
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ:

Segments UV and WZ are parallel segments that intersect with line ST at points Q and R, respectively.

According to the given information, segment UV is parallel to segment WZ, while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Theorem. Finally, angle VQT is congruent to angle WRS by the ________ Property.

Which property of equality accurately completes the proof?

А Reflexive
B Substitution
C Subtraction
D Transitive

0.75 (6+d)=12 step by steP

What is the numerical coefficient of the a^4 b^4 term in the expansion of (1/3a^2 - 2b)^6

enter your answer, in the simplest fractional form, in the box​

please find the value of x​

Write an equation of the line passing through point P(4, -6) that is perpindicular to the line y= -3.​

Find the area of the small rectangle. 2x + 3 x + 6 x - 5

There are 90 people in a group.
A sixth of the people in the group are men.
The number of women in the group is 2 times the number of men in the group
The rest of the people in the group are children.
the number of children in the group : the number of men in the group = n: 1
Work out the value of n.
You must show how you get your answer.

LEASE HELP ME WITH THESE 3 QUESTIONS, DUE NOW! WILL GIVE BRAINLIST
QUESTIONS:

1. The seventh grade class held an end of the year dance. Of the 300 seventh graders, 246 decided to attend. What percent of the seventh grade class attended the end of the year dance? *
A. 1.12%
B. 85%
C. 82%

2. A farmer decides to sell 32 pounds of his small 96-pound potato crop. What percent of the crop did he sell? *
A. 33%
B. 30%
C. 3%

3. Tolu is reading a new novel. He has read 173 out of 480 pages. About what percent of the book has he read? *
A. 33%
B. 36%
C. 35%
D. 28%

What is the value of
1.6x1094
32x107
in scientific notation?
07.5x100
5.0x10
5.0x100
0.5x10?
I need help

9. Ricardo bought a pair of shoes for $55.60 and a hat for $9.78. How much did he spend in all? If he paid with 4 twenty- dollar bills, how much change did he get?




please help me!!! I'll mark brainiest!​

The ratio of money in Terry's bank account to Faye's bank account was 3:5.
Terry then put £220 in his account and Faye withdrew £300 from her account.
They now had the same amount in their accounts.
How much did they initially have altogether?

which point lies on the graph of y=3/4x -2?

1. Two eighth grade classes are selling tickets to raise money for their school fundraiser.
• One class is selling tickets for $3.50 each and has already raised $250.
• The other class is selling tickets for $2.25 each and has already raised $300.
How many tickets does each class have to sell so that the total amount raised is the
same for both classes?

ASAP WILL GOVE BRAINLIEST FO YOU EXPLAIN AND GIVE ME ANSWER ASAP

In eight minutes josh was able to type 496 words what’s he typing speed per minute

If 7r + 5s = 35, then r = HELP THIS WAS DUE YESTERDAY

help plsss .....!!!!

9(x+3)=4x-3
plz show steps

Laura needs to buy chips and soda for the guest at her party. Each large bag of chips cost 2.40 and each large bottle of soda costs 2.00. She had 48.00 to spend. Which graph represents the number of bags of chips and bottles of soda that Laura can buy?

Given the following function, find f(-4), f(0), and f(4).
f(x) = x + 2

f(-4)=
f(0) =
f(4)=

Rewrite in simplest terms: -7(10p-10)+3(-6p-6)

start a convo and make friends cause why not​

f(x)= -3/4x+6

Find the inverse I need help pretty bad please help!!

Use a proportion to find each value.
a. 2% of 180
b. What percent is 17 out of 40

please help me!

Which table represents a linear function?

evaluate 24−8x when x=−2

URGENT: Solve the following: (5x10^9)x(7x10^5)
A. 3.5 x 10^14
B. 3.5 x 10^15
C. 3.5 x 10^5
D. 3.5 x 10^4

Which expression is equal to (5−2i)−(1+3i)

I need help with this, I´ĹL GIVE THE FIRST ANSWER BRAINLIEST