Prove that `g(x,y) = xlog(y/x)` is homogenous, what is the degree? Verify Euler's Theorem for g.

Prove that f(x,y) =x^(3) - 2x^(2)y + 3xy^(2) + y^(3) is homogenous, what is the degree? Verify Euler's Theorem for f.

f(x,y)=(1)/(x+y) is a homogeneous function of degree

Show that F(x,y)=(x^2+5xy-10y^2)/(3x+7y) is a homogeneous function of degree 1.

Prove that the DE is (3xy+y^2)dx+(x^2+xy)dy=0 a homogeneous DE of degree0.

Verify Euler's theorem for w = x ^(2) sin ((y)/(x)).

True or false: The function F(x,y)=ysin(y/x)-x is a homogenous function of degree 1.

True or false: A differential equation of the form (dy)/(dx)=g(x,y) where g(x,y) is a homogenous function of degree zero, can be solved by the substitution y=vx .

If f(x,y)= (x-y)/(x+y) then write the degree of the homogenous function (df)/(dy) .

Fill ups The function phi(x,y)=x^2y+xy^2 is homogenous of degree……….. .