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:
i dont know toooo pls answer it fast......................................
Step-by-step explanation:
i need it..........................
Answer:
x=63
Step-by-step explanation:
The two interior angles add up the the exterior angle, so 51+x+12=2x. From there, solve to get x=63. Hope this helped!
<h2>
Good evening ,</h2>
<em><u>Answer</u></em>:
q=-10
<em><u>Step-by-step explanation:</u></em>
D:y=-3x+q
let’s find q
A(-4,2)∈D ⇔ 2=-3(-4)+q ⇔ q=-10
then D:y=-3x-10
look at the photo for more details.
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:)
