Can some one PLEASE give me brainliest

Given the Homogeneous equation x^2ydy+xy^2dx=0, use y=ux, u=y/x and dy=udx+xdu to solve the differential equation. Solve for y.

scZoUnD [109]

Answer:

$y=\frac{C}{x}$ .

Step-by-step explanation:

Given homogeneous equation

$x^2ydy+xy^2dx=0$

$\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{xy^2}{x^2y}$

Substitute y=ux , $u=\frac{y}{x}$

$\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{y}{x}$

Now,

$u+x\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{\mathrm{d}y}{\mathrm{d}x}$

$u+x\frac{\mathrm{d}u}{\mathrm{d}x}=-u$

$\frac{\mathrm{d}u}{\mathrm{d}x}=-2u$

$\frac{du}{u}=-\frac{dx}{x}$

Integrating both side we get

lnu=-2lnx+lnC

Where lnC= integration constant

$lnu+ln{x}^2=lnC$

$lnux^2=lnC$

Cancel ln on both side

$ux^2=C$

Substitute $u=\frac{y}{x}$

Then we get

xy=C

$y=\frac{C}{x}$ .

Answer: $y=\frac{C}{x}$ .

8 0

3 years ago

An Internet and cable-television supplier surveyed a random sample of their customers. The results are shown in the table.

IrinaVladis [17]

For the statement "....A 4-column table with 3 rows. The first column has no label with entries internet, cable television, or total. The second column is labeled satisfied with entries ..." statement about the two-way frequency table that is true is About one-fourth of the cable-television customers are not satisfied. Option D.

This is further explained below.

<h3>What is a two-way frequency table?</h3>

Generally, A two-way table may be used to show the frequency of occurrence of two categories. A row represents a single category, whereas a column represents a different category.

In conclusion, There are 3,141 customers in total, of which 2,032 are internet customers and 1,109 are cable customers.

Read more about the two-way frequency table

brainly.com/question/12576014

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7 0

2 years ago

As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular

spayn [35]

Answer:

10 milligrams of Medication A

Step-by-step explanation:

We'll write proportions/ratios for this:

20:16 is the usual proportion, and x:8 is this week's dose. The ratio from A to B has to be equal, so

20/16 = x/8

Cross-multiply:

(20)(8) = (16)(x)

160 = 16x

divide both sides by 16

x = 10

Please let me know if you have questions about this answer.

5 0

3 years ago

How do i draw two number lines that show 0.20 and 1/5 are equivalent?

leonid [27]

The frist line may be one with the numbers 0, 1 and 2 and 10 divisions (marks at equal distance) between each integer. Each division will be equal to 0.1 units and then you can mark the second division from the zero point to the right as the 0.20 mark.

The other line must have the same integers, 0 , 1 and 2 placed in identical form as the first line. Then
   - draw an inclined straight line since the point zero,
   - mark 5 points in the inclined lined equally spaced over the line.
   - draw a sttraight line from the 5th point to the point with the mar 1 over the base number line.
   - draw a parallel line to the previous one passing trhough the second point of the inclined line and mark the point where this parallel touchs the base number line. This point shall be at the same distance from zero than the 0.2 mark was in the first number line, meaning that 0.2 and 1/5 are equivalent.

6 0

3 years ago

Which of the following is a coterminal angle of 138°? A.) 438° B.)-136° C.) -582° D.) 228°

GaryK [48]

Answer: I think the correct answer is D.

8 0

3 years ago

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