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\delta\left ( x,y \right )= x^{1/2}y^{3/2}+xy is a homogeneous function of degree

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As we learnt

 

Homogeneous Differential Equation -

A function

f\left ( x,y \right ) 

is called homogeneous function of  degree n, if

f\left (dx,dy \right )=d^{n}\left ( x,y \right )

- wherein

eg:

f\left ( x,y \right )=x^{2}y^{2}-xy^{3}

 

 

 

\delta \left ( dx,dy \right )=\left ( dx \right )^{1/2}\left ( dy \right )^{3/2}+\left ( dx \right )\left ( dy \right )= d^{2}x^{1/2}y^{3/2}+d^{2}xy

\Rightarrow \delta \left ( dx,dy \right )= d^{2}\left ( x^{1/2}y^{3/2}+xy \right )= d^{2} \delta \left ( x,y \right )

So degree = 2.


Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

4

Posted by

Himanshu

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