Question

二元函数问题,求f(x,y) 1. f(x+y,x-y)=2(x^2+y^2)e^(x^2-y^2) 2. f(x+y,xy)=2x^2+xy+2y^2？

Answer 1

1. f(x+y,x-y)=2(x^2+y^2)e^(x^2-y^2)
令x+y=m,x-y=n

则x=(m+n)/2,y=(m-n)/2

所以

f(m,n)

=2[(m+n)^2/4 + (m-n)^2/4] * e^[(m+n)^2/4 - (m-n)^2/4]

=(m^2+n^2) * e^(mn)

所以f(x,y）=(x^2+y^2) * e^(xy)

2. f(x+y,xy)

=2x^2+xy+2y^2

=2(x^2+y^2)+xy

=2[(x+y)^2-2xy]+xy

=2(x+y)^2-3xy
,8,
二元函数问题,求f(x,y)

1. f(x+y,x-y)=2(x^2+y^2)e^(x^2-y^2)