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Dmitrij [34]
2 years ago
13

1) Find the general solution to the following differential equation x^3•y’- y = 0

Mathematics
1 answer:
maxonik [38]2 years ago
6 0

Answer:

y(x) = c_1 e^(-1/(2 x^2))

Step-by-step explanation:

Solve the separable equation x^3 (dy(x))/(dx) - y(x) = 0:

Solve for (dy(x))/(dx):

(dy(x))/(dx) = y(x)/x^3

Divide both sides by y(x):

((dy(x))/(dx))/y(x) = 1/x^3

Integrate both sides with respect to x:

integral((dy(x))/(dx))/y(x) dx = integral1/x^3 dx

Evaluate the integrals:

log(y(x)) = -1/(2 x^2) + c_1, where c_1 is an arbitrary constant.

Solve for y(x):

y(x) = e^(-1/(2 x^2) + c_1)

Simplify the arbitrary constants:

Answer:  y(x) = c_1 e^(-1/(2 x^2))

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Answer:

y=6

Step-by-step explanation:

x=20

y=10

x=15 > 20x=15

x=15/20

x=3/5

y=10(3/5)

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2 years ago
Tevon,leah,and beth are playing a computer game. Trevon scored -8. Beth's score was 3/4 of trever's score, and leah's score was
faust18 [17]

Answer:

Trevon scored -8.

Beth's score was 3/4 of trever's score = -8 *3/4 = -6

leah's score was 1/4 of beth's score. = -6 *1/4 = -1.5

Leah's score was -1.5


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3 years ago
80% of the 55 coffee mugs at Kari's Pancake House are dirty. How many dirty coffee mugs are there at the pancake house?
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Answer:

44

Step-by-step explanation:

80% of 55=44

4 0
2 years ago
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Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
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Answer:

34 - 25 = 9

Step-by-step explanation:

7 0
3 years ago
The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
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+2

-4 (Second integer)


+4

-2 (Third integer)


Integers: -6, -4, -2

Equation: x = (x+2) + (x+4)

8 0
2 years ago
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