Originally Posted by
pepsi hello,
i am asked to prove that if z= [f(y/x)]/x then
...pls read [z_x] as the partial of z w.r.t.x...
x[z_x] + y[z_y] + z = 0 (*)
i have tried totally differentiating
dz = {-[1/x^2][f(y/x)] + [1/x][f_x] }dx + [1/x][f_y]dy
but then i get from the LHS of (*) that [1/x][f_x] }dx + [1/x][f_y]dy = ?
I am given clues for two methods that i may follow:
1) set y/x =v
and
2) to use the fact that for a homogenous function g(x,y) of nth order it is true that x[g_x] + y[g_y] = 0
i am stuck