Word Count : 401

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दी गई अवकल समीकरण है: $$ z(x^2 - y^2 - z^2) \, dx + (x + z)xz \, dy + x(z^2 - x^2 - xy) \, dz = 0 $$ इसे हम इस रूप में लिख सकते हैं: $$ M\,dx + N\,dy + P\,dz = 0 $$ जहाँ $$ M = z(x^2 - y^2 - z^2), \quad N = (x+z)xz, \quad P = x(z^2 - x^2 - xy) $$ चरण 1: अवकलनीयता की जाँच त्रि-चर अवकल समीकरण $M\,dx + N\,dy + P\,dz = 0$ केवल तभी पूर्ण अवकलनीय होता है यदि: $$ \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}, \quad _________ _____ __________ _______ _____ __________ _____ ___.
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