Maths-
General
Easy

Question

If u equals f left parenthesis x comma y right parenthesis is a homogeneous function of order n.

I) x fraction numerator straight partial differential u over denominator straight partial differential x end fraction plus y fraction numerator straight partial differential u over denominator straight partial differential y end fraction equals n u

II) x squared fraction numerator straight partial differential squared u over denominator straight partial differential x squared end fraction plus 2 x y fraction numerator straight partial differential squared u over denominator straight partial differential x straight partial differential y end fraction plus y squared fraction numerator straight partial differential squared u over denominator straight partial differential y squared end fraction equals n left parenthesis n minus 2 right parenthesis u

III) x fraction numerator straight partial differential squared u over denominator straight partial differential x squared end fraction plus y fraction numerator straight partial differential squared u over denominator straight partial differential x straight partial differential y end fraction equals left parenthesis n minus 1 right parenthesis fraction numerator straight partial differential u over denominator straight partial differential x end fraction

Which of the above statements is correct ?

  1. Only I
  2. Only II, III
  3. Only I and III
  4. I, II, III

The correct answer is: Only I and III

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