3 years ago

What is the slope of a line that is parallel to the graph of 5x+4y=y?

Mathematics

1 answer:

torisob [31]3 years ago

7 0

Answer:

-5/3

Step-by-step explanation:

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68+(-41)=? Solved and show how you got the answer.

mars1129 [50]

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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

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$lnux^2=lnC$

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$ux^2=C$

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

Then we get

xy=C

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

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3 years ago

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