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)
Considering the given graph, the number of solutions for the system of equations is given by:
b.) one
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In a graph, the number of solutions is given by the number of times the lines intersect. Hence, in this problem, the system has one solution, and option b is correct.
More can be learned about a system of equations at brainly.com/question/24342899
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Let one odd integer = x
other odd integer = x +2
Sum = x + x+2 = -44
=> 2x + 2 = -44
=> 2x = -44 -2 = -46
=> x = -46/2 = -23
x+2 = -23 + 2 = -21
Integers are -23 and -21
Answer:
<4 = 22
Step-by-step explanation:
<4 = x
x + 158 = 180
x = 22
