Question

help me in homogeneous equation

Answer 1

determine in each exercise whether or not the equation/function is homogeneous. if it is homogeneous, state the degree of teh function

Answer 2

\[1. y` = \frac{ 2y^4+x^4 }{ xy^3}\]

Answer 3

\[2. y` = \frac{ (x^2+y) }{ x^3 }\]

Answer 4

\[3. y` = \frac{ x^2+y }{ xy }\]

Answer 5

4. \[y`= \frac{ x^2 }{ y }\]

Answer 6

\[5. y` = \frac{ y }{ x + \sqrt{xy} }\]

Answer 7

@kittiwitti1

Answer 8

Hi

Answer 9

Look at the right side of the given equation.

```
Replace x by kx
Replace y by ky
```
what do you get ?

Answer 10

\[= \frac{ ky^4 +kx^4 }{ kxky^3}\]

Answer 11

@ganeshie8 hey

Answer 12

simplify the fraction a bit by factoring out k's

Answer 13

also you have it wrong

Answer 14

\[k(y^4+x^4)/k(xy^3)\]

Answer 15

x^4


replacing x by kx gives you (kx)^4
not just kx^4

Answer 16

\(\large y' = \frac{ 2y^4+x^4 }{ xy^3} \)

replace y by ky and x by kx

\(\large y` = \frac{ 2(ky)^4+(kx)^4 }{ kx(ky)^3} \)

Answer 17

use the property
\[(ab)^n=a^nb^n\]

Answer 18

\[y`` = \frac{ 2(ky)^5+(kx)^5 }{ kx(ky)^4}\]

Answer 19

??