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: The Selective Service Act requires all men between the ages of 21 and 30 to register for military service.
Step-by-step explanation:
In this case just do it left to right, as multiplication comes before addition/subtraction. So 7x3x2+5-3=21x2+5-3=42+5-3=47-3=44=k.
Answer:
-3 1/2 > -4.5
Step-by-step explanation:
1.5 > 2 1/2 False
1/2 > 0.5 False
-2.5 > -1.5 False
-3 1/2 > -4.5 True
1.5 > 2 1/2
1/2 = 0.5
2 + 0.5 = 2.5
1.5 is not > 2.5
1.5 < 2.5
1/2 > 0.5
1/2 = 0.5
0.5 is not > 0.5
0.5 = 0.5
-2.5 > -1.5
Negative numbers are oposite of positive numbers when using inequalities. Just as 0 < 1, -1 < 0.
-2.5 is not > -1.5
-2.5 < -1.5
-3 1/2 > -4.5
1/2 = 0.5
3 + 0.5 = 3.5
-3.5 > -4.5
