Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
Answer:
300
Step-by-step explanation:
find the sum of area of all sides
The number of words james can type in 6 minutes at the same rate is 360 words
Given:
Number of minutes to type 150 words = 2.5 minutes
let
number of words James can type in 6 minutes = x
Equate the ratio of the number of words to number of minutes
150 : 2.5 = x : 6
150/2.5 = x/6
cross product
150 × 6 = 2.5 × x
900 = 2.5x
x = 900/2.5
x = 360 words
Therefore, the number of words james can type in 6 minutes is 360 words
Learn more about ratio:
brainly.com/question/16981404
9514 1404 393
Answer:
geometric sequence
Step-by-step explanation:
The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...
an = 3(-4)^(n-1)
so the sum can be written as ...
(Note the summation starts at n=0, corresponding to a first term of 3.)
