Show that the equation M(x,y)dx+N(x,y)dy = 0 has an integrating factor which is a function of ratio of x and y.?
1 Answer
Aug 13, 2018
If there exists the I.F.
So, applying the I.F.:

# (M mu)_y = M_y mu  x /y^2 M mu' qquad bbbA# 
# (N mu)_x = N_x mu + N 1/y mu' qquad bbbB#
For this to be an I.F., the mixed partials must be equal:
Therefore, for the I.F.