- #1

- 181

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(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.