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3 years ago

Find general solution for y'' +y'-6y=12(e^3t+e^-2t)

2 answers:

6 0

Homogeneous solution: y′′+y′−6y=0 yields the characteristic equation r2+r−6=0 ⇒ r=−3,2 So homogeneous part is yc=C1e−3t+C2e2t. Non-homogeneous solution: y′′+y′−6y=12e3t+12e−2t Use the method of undetermined coefficients. Suppose yp=Ae3t+Be−2t is a solution, so you have yp=Ae3t+Be−2ty′p=3Ae3t−2Be−2ty′p=9Ae3t+4Be−2t Substitute into the original equation: (9Ae3t+4Be−2t)+(3Ae3t−2Be−2t)−6(Ae3t+Be−2t)6Ae3t−4Be−2t=12e3t+12e−2t=12e3t+12e−2t This tells you that A=2 and B=−3, and so your non-homogeneous part is yp=2e3t−3e−2t. Your final solution would be the sum of the non/homogeneous parts, or y=yc+yp

castortr0y [4]3 years ago

3 0

Am i correct? Your solution would be y=yc+yp

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The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ

Nutka1998 [239]

Answer:

equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

(x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

-18-3 = -21
-18-1 = -19
-18+1 = -17
-18+3 = -15

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

(x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

4x +12 = -72 . . . . . collect terms

4x = -84 . . . . . . . . subtract 12

x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

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4 years ago

Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer

lina2011 [118]

Step-by-step explanation:

The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:

(y - k)^2 = 4 * f * (x - h)

In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:

y^2 = 4 * f * x

= 4 * (-1.3) * x

= -5.2x

The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.

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1 year ago

Mike measured the stage where his band was going to play to determine if it is a right triangle. Does the stage with side length

katrin [286]

Answer:

let

hypotenuse[h]=60ft

base[b]=36ft

perpendicular [p]=48ft

by using Pythagoras law

p²+b²=h²

48²+36²=60²

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3 years ago

Calculate the principal amount which earns $500 simple interest over 3 Years at a rate of 8% p.a round to the nearest cent

timama [110]

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Interest for one year is $166.67
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Principal amount is $2083.33

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slega [8]

B. -3 and 5

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