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

Answers

Answer 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]


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Answers

Answer:

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Step-by-step explanation:

The world has made it a basis that most people eat 3 meals a day.

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Answers

Answer:

1x + 46 or x + 46

Step-by-step explanation:

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???

Step-by-step explanation:

???

Evaluate: -8/9 + 4/9 - 2/9

A. -14/9
B. -2/3
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Answers

Answer:

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Step-by-step explanation:

Add the first two then subtract

The answer to the equation is B, [tex]-\frac{2}{3}[/tex]

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Answers

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Step-by-step explanation:

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A 3-yard roll of butcher paper costs $8.55. What is the price per foot?

Answers

Answer:

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Step-by-step explanation:

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Answer:

$2.85 per foot

Step-by-step explanation:

all u gotta do is 8.55/3

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Help and brainliest? :(

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Each exterior angle is 120 degrees

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DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA

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Answer:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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answer: each apple cost 2$

Answer:

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The perimeter of a kite can be found using the formula P = 2S + 2L. Which equation expresses S in terms of P and L?

Answers

Answer:

Step-by-step explanation:

P = 2S + 2L

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Answer:

0.5P - L

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Original Equation:

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Step-by-step explanation:

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Given here: Slope intercept form

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