## anonymous 3 years ago homogeneous equations....how to find degree???

1. anonymous

can u explain by example??

2. anonymous

do we have to convert equation to y/x form everytime??

3. anonymous

yes

4. anonymous

what i know is that if we have equation like|dw:1354030150259:dw|

5. anonymous

we find degree by |dw:1354030245650:dw|

6. anonymous

its a function

7. anonymous

say f(x,y)

8. anonymous

the denominator x cancels numerator x n what we get degree as 2

9. anonymous

since x has power 2

10. anonymous

u catchin me?

11. anonymous

but in another question

12. anonymous

$x^n f1(y/x)+y^-n f2(x/y)$

13. anonymous

degree is considered both + and - n

14. anonymous

i want to know in what form of fraction do we have to exactly convert an equation to find degree?? x/y or y/x?? hope u get what m askin

15. across

A function $$f$$ is said to be homogeneous of degree $$k$$ if $$f(\alpha\mathbf{x})=\alpha^kf(\mathbf{x})$$. In your case,$f(\alpha x,\alpha y)=\frac{\alpha^3x^3+\alpha^3y^3}{\alpha x-\alpha y}=\alpha^2\frac{x^3+y^3}{x-y}=\alpha^2f(x,y).$

16. anonymous

@across thanx for ya help aneways