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ddd [48]
3 years ago
11

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

Mathematics
1 answer:
lozanna [386]3 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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kherson [118]
There is no graph how am I supposed to answer this
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3 years ago
3m + n =7<br> m + 2n = 9​
harkovskaia [24]

Answer:

n = 4, m = 1

Step-by-step explanation:

Given the 2 equations

3m + n = 7 → (1)

m + 2n = 9 → (2)

Rearrange (2) expressing m in terms of n, by subtracting 2n from both sides

m = 9 - 2n → (3)

Substitute m = 9 - 2n into (1)

3(9 - 2n) + n = 7 ← distribute left side

27 - 6n + n = 7 ← simplify left side

27 - 5n = 7 ( subtract 27 from both sides )

- 5n = - 20 ( divide both sides by - 5 )

n = 4

Substitute n = 4 into (3) for corresponding value of m

m = 9 - (2 × 4) = 9 - 8 = 1

Thus m = 1 and n = 4

6 0
3 years ago
I need help answering
I am Lyosha [343]

8(1/4) - 1 + 0.5(10)

8/4 - 1 + 5

2 - 1 + 5

1 + 5 = 6

4 0
4 years ago
Read 2 more answers
I need someone to Evaluate 271,000√3.<br><br> Make it into a fraction
Debora [2.8K]

Answer:

6 1615/15377

Step-by-step explanation:

271,000√3 = 469385.768851

Turn that into a fraction 469385/ 768851

Simplify.

3 0
3 years ago
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Nine cars (3 Pontiacs [labeled 1-3], 4 Fords [labeled 4-7], and 2 Chevrolet's [labeled 8-9]) are divided into 3 groups for car r
STatiana [176]

Answer:

The number of different ways to arrange the 9 cars is 362,880.

Step-by-step explanation:

There are a total of 9 cars.

These 9 cars are to divided among 3 racing groups.

The condition applied is that there should be 3 cars in each group.

Use permutation to determine the total number of arrangements of the cars.

  • For group 1:

       There are 9 cars and 3 to be allotted to group 1.

       This can happen in ^9P_{3} ways.

        That is, ^9P_{3}=\frac{9!}{(9-3)!} =504 ways.

  • For group 2:

       There are remaining 6 cars and 3 to be allotted to group 2.

       This can happen in ^6P_{3} ways.

        That is, ^6P_{3}=\frac{6!}{(6-3)!} =120 ways.

  • For group 3:

       There are remaining 3 cars and 3 to be allotted to group 3.

       This can happen in ^3P_{3} ways.

        That is, ^3P_{3}=\frac{3!}{(3-3)!} =6 ways.

The total number of ways to arrange the 9 cars is: ^9P_{3}\times ^6P_{3}\times ^3P_{3}=504\times120\times6=362880

Thus, the number of different ways to arrange the 9 cars is 362,880.

7 0
4 years ago
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