Originally Posted by
nameck Question:
(1 - x - z)dx + dz = 0
let M = (1 - x - z) ; N = 1
dM/dz = -x ; dN/dx = 0
hence, not exact.
integrating factor...
1/N[ dM/dz - dN/dx ] = 1[-x]
.................................= -x
e^ ∫-x dx = e ^ [(-x^2)/2]
times integrating factor with DE..
{e ^ [(-x^2)/2] -x e ^ [(-x^2)/2] - z e ^ [(-x^2)/2]}dx +
e ^ [(-x^2)/2]dz = 0
dM/dz = -e ^ [(-x^2)/2] ; dN/dx = -xe ^ [(-x^2)/2]
the problem is, i calculated the integrating factor.. but, the equations still not the exact calculation.