3 years ago

What is the answer for this question:

Mathematics

1 answer:

Sergio [31]3 years ago

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3 years ago

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

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3 years ago

Where do you find the solution to a system of liner equations??

oksano4ka [1.4K]

Answer:

The intersection of both lines.

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What is the constant in this expression? 3 x squared minus 2 x + y minus 4

cupoosta [38]

What are the numbers x and y are sopposed to be?

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The sum of a number w and 3 is less than or equal to ten.

Assoli18 [71]

W + 3 ≤ 10

This is the symbol for less than or equal ≤

w + 3 ≤ 10

w ≤ 10 - 3

w ≤ 7

Can't find an answer for w from the options.

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3 years ago