Question

1.7: If u is a homogeneous function of degree n in x and y then? ​

Answer 1

Answer:

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Question

If F(u)= f(x,y,z) be a homogeneous function of degree n in x,y,z, then x∂x∂u+y∂y∂u+z∂z∂u=

A

F(u)F(u)

B

n F (u)

C

nu

D

None of these

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Solution

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Correct option is B)

A function f is called homogeneous of degree n, then it will satisfy the equation-

f(tx,ty,tz)=tnf(x,y,z)

f(x,y,z)=F(u)

Let,

p=tx

q=ty

r=tz

Therefore,

dtd(p,q,r)=ntn−1f(x,y,z)

∂p∂fdtdp+∂q∂fdtdq+∂r∂fdtdr=ntn−