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:
H=5.0 (to the nearest 10th)
Step-by-step explanation:
≈4.99846
Rachel and her sister Fran together can paint the living room in 
hours
Given that
Rachel can paint half of the living room in 1 hour
Fran can paint 
th part of the living room in 1 hour
Let's assume together they paint the living room in x hours
⇒ together they can paint 
th part of the living room in 1 hour
By proportions,
⇒
+= {using operation proportions and addition}
⇒
=
⇒x=
⇒ together they can paint th part of the living room in 1 hour
It means, Rachel and her sister Fran together can paint the living room in hours
Learn more about paint here:
brainly.com/question/15277377
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Find the two numbers. Algebra -> Customizable Word Problem Solvers -> Numbers -> SOLUTION: The difference of two positive numbers is 8. The larger is twice the smaller decreased by 7.
