If f(x,y)is a function satisfying euler’ s theorem then?
Posted: Thu Jul 14, 2022 9:29 am
a) \(x^2\frac{∂^2 f}{∂x^2}+2xy \frac{∂^2 f}{∂x∂y}+y^2 \frac{∂^2 f}{∂y^2}=n(n-1)f\)
b) \(\frac{1}{x}^2\frac{∂^2 f}{∂x^2}+\frac{2}{xy} \frac{∂^2 f}{∂x∂y}+\frac{1}{y}^2 \frac{∂^2 f}{∂y^2}=n(n-1)f\)
c) \(x^2\frac{∂^2 f}{∂x^2}+2xy \frac{∂^2 f}{∂x∂y}+y^2 \frac{∂^2 f}{∂y^2}=nf\)
d) \(y^2\frac{∂^2 f}{∂x^2}+2xy \frac{∂^2 f}{∂x∂y}+x^2 \frac{∂^2 f}{∂y^2}=n(n-1)f\)
b) \(\frac{1}{x}^2\frac{∂^2 f}{∂x^2}+\frac{2}{xy} \frac{∂^2 f}{∂x∂y}+\frac{1}{y}^2 \frac{∂^2 f}{∂y^2}=n(n-1)f\)
c) \(x^2\frac{∂^2 f}{∂x^2}+2xy \frac{∂^2 f}{∂x∂y}+y^2 \frac{∂^2 f}{∂y^2}=nf\)
d) \(y^2\frac{∂^2 f}{∂x^2}+2xy \frac{∂^2 f}{∂x∂y}+x^2 \frac{∂^2 f}{∂y^2}=n(n-1)f\)