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:
6 cm^2
Step-by-step explanation:
Area of Rectangle is L*W
L=3 and W=2
3*2=6
Answer:
For example, a common equation, y=mx+b y = m x + b
Step-by-step explanation:
is a linear function because it meets both criteria with x and y as variables and m and b as constants.
Dup= 72 miles
<span>ddown= 120 miles </span>
<span>v= riverspeed </span>
<span>rup= 32mph - v </span>
<span>rdown= 32mph + v </span>
<span>t both ways= t </span>
<span>d=r*t </span>
<span>d/r=t </span>
<span>t=ddown/rdown </span>
<span>t=dup/rup </span>
<span>dup/rup = ddown/rdown </span>
<span>(72)/(32-v)=(120)/(32+v) </span>
<span>3840-120v=2304+72v </span>
<span>1536=192v </span>
<span>v=8</span>
<u>67x + 90</u>
10
Please tell me im smart, lol
