2 years ago

Which ratio is not equivalent to the other A)6:15 B)6 to 15 C) 6/15 D)15/6

Mathematics

1 answer:

Andreyy892 years ago

7 0

Answer:

Step-by-step explanation:

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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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