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3 years ago

What is the solution for this system use the graphics method ? Help me plz

Mathematics

1 answer:

MAVERICK [17]3 years ago

6 0

Answer:

(-3,29)

Step-by-step explanation:

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Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

Help me smart math people

Paul [167]

Answer:

48 because i720 divided into 15 groups calculate to 48

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3 years ago

Elena's aunt bought her a $200 savings bond when she was born. When Elena is 20 years old, the bond will have earned 110% in int

natulia [17]

Step-by-step explanation:

$157.50

i HOPE THIS HELP YOU

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3 years ago

Help can somone help please.

disa [49]

Answer:

0.7

Step-by-step explanation:

5(9n-6)

5×9n-5×6

45n-30

45n/45 -30/45

or 45n÷45-30÷45

n= 0.6666

0.7

hope dis helps!!!!!

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2 years ago

2. Is the expression 2 • 4' equal to the expression 8"? Explain your answer.

liberstina [14]

Yes, this is because 2*4 equals 8

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3 years ago