\(\large 1.\) GIVEN: \(\large F(v^2-x^2,v^2-y^2,v^2-z^2)=0\)

where \(\large v\) is a function of \(x,y,z\)

\(\textbf{SHOW THAT:}\) \[\large \frac{1}{x}\frac{\partial v}{\partial x}+\frac{1}{y}\frac{\partial v}{\partial y}+\frac{1}{z}\frac{\partial v}{\partial z}=\frac{1}{v}\]

\(\large 2.\) GIVEN: \( V=f(X,Y,Z) \) is a homogeneous function in \(x,y,z\) of degree \(\boxed{n}\)

where \( X=\dfrac{\partial V}{\partial x}, Y=\dfrac{\partial V}{\partial y}, Z=\dfrac{\partial V}{\partial z}\)

\(\textbf{SHOW THAT:}\) \[\large X\frac{\partial V}{\partial X}+Y\frac{\partial V}{\partial Y}+Z\frac{\partial V}{\partial Z}=\frac{n}{n-1}V\]

Now for the second one, i understand that the Euler's theroem is necessary but i can't proceed in a definite direction from there

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

## Comments

Sort by:

TopNewest@Aritra Jana @Calvin Lin i am opening brilliant after 3 years. i think i have 2 solutions to problem 1 but i am not being able to post a picture.plz help

Log in to reply

Approaches

`![](URL)`

to display images.Log in to reply

What have you done? What have you tried?

Can you show your working?

Log in to reply

@Aritra Jana sorry but I don't know much about partial derivatives.

Log in to reply

oh sorry, my bad. although , could you help me by tagging some who you think have a certain degree of knowledge in this field?

Log in to reply

@Otto Bretscher

Log in to reply

@Calvin Lin @Chew-Seong Cheong @Agnishom Chattopadhyay @Parth Lohomi

Log in to reply