The general solution of the given differential equation be
For given question,
We have been given a differential equation y'' − y' − 12y = e^(4x)
We need to solve the given differential equation by undetermined coefficients.
We can write given differential equation as where
First solve the corresponding homogeneous differential equation:
y'' - y' - 12y = 0
The characteristic equation is:
m² - m - 12 =0
Let's find the roots of above quadratic equation by factorization.
⇒ m² - m - 12 = 0
⇒ (m - 4)(m + 3) = 0
⇒ m - 4 = 0 OR m + 3 = 0
⇒ m = 4 OR m = -3
Hence the complementary solution is,
Let the general solution of a second order homogeneous differential equation be
The unknown functions C1(x) and C2(x) can be determined from the system of two equations:
from (1),
Substitute this value in equation (2)
and
and
Therefore, the general solution of the given differential equation be
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Answer:
x = 16
Step-by-step explanation:
From the first statement, we can say that:
Angle A is equal to angle D,
Angle B is equal to and E.
Since measure of Angle B and E are given and they are equal, we equate them and solve for x.
Hence x = 16
50% because when you take out the first marble witch is probably blue since there are more blue you would have 2 blue and 2 green so the chance would be 50%
<h3>
Answer: C) 6</h3>
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Explanation:
The weird looking E symbol is the greek uppercase letter sigma. It refers to a sum.
It tells us to add up terms in the form (-1)^n*(3n+2) where n is an integer ranging from n = 1 to n = 4.
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If n = 1, then we have
(-1)^n*(3n+2) = (-1)^1*(3*1+2) = -5
Let A = -5 as we'll use it later.
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If n = 2, then
(-1)^n*(3n+2) = (-1)^2*(3*2+2) = 8
Let B = 8 since we'll use this later as well
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If n = 3, then
(-1)^n*(3n+2) = (-1)^3*(3*3+2) = -11
Let C = -11
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If n = 4, then
(-1)^n*(3n+2) = (-1)^4*(3*4+2) = 14
Let D = 14.
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We'll add up the values of A,B,C,D to get the final answer
A+B+C+D = -5+8+(-11)+14 = 6
This means that
Answer:
<h3>Hope this helps...</h3><h3>have a nice day/night!!</h3>