Question

What is homogenous function?
Please explain me in easy way:)

Answer 1

is this a differential equation question?

Answer 2

no
i m only a beginner of calculus
i want only some explanation:)

Answer 3

sorry i got aw snapped..let me rewrite..

Answer 4

np:)

Answer 5

to determine if a function is homogeneous or not, substitute x and y with \(\lambda x\) and \(\lambda y\) respectively. after that, simplify the function. if the function becomes in the form \(\lambda ^n f(x,y)\) then it is a homogeneoous function.

for example

f(x,y) = x^3 + y^2 + 1

if i substitute i get
\[(\lambda x)^3 + (\lambda y)^3 + 1\]
\[\implies \lambda ^3 x^3 + \lambda ^2 y^2 +1 \]
\[\implies \lambda^2 (\lambda x^3 + y^2) +1\]
this does not look like \[\lambda^n f(x,y)\]

this is how a homogeneous function should look like

f(x,y) = x^2 + y^2

substitute..

\[(\lambda x)^2 + (\lambda y)^2\]
\[\implies \lambda ^2 x^2 + \lambda^2 y^2\]
\[\implies \lambda ^2 (x^2 + y^2)\]

this looks like \(\lambda ^2 f(x,y)\) right? therefore it is homogeneous..

does that help?

Answer 6

...that nostalgic feeling of writing tutorials =))

Answer 7

gt it
thanx:)

Answer 8

welcome ^_^ and glad you got it...i was worried i wasnt articulate enough

Answer 9

^_^