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:
d=252m, u dint put the speed it was rolling at from point B to C so I could only solve for A to B. However if you use the formula below you can find the distance from B to C and add that to A to B giving the total distance rolled.
Step-by-step explanation:
d=vt
v=14m/s
t=18s
d= vt, (14m/s)(18s)
d=252m
Answer:
ok so this can be represented as
7.75x+675=1062.50
-675
7.75x=387.5
divide by 7.75
x=50
Hope This Helps!!!
Answer:
-49
Step-by-step explanation:
you can first divide both sides by -6
so
-12 = y+37
so y = -12-37 = -49
