(6xy^7+cosy)dx+(2kx^2y^7-1-xsiny)dy=0

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Solution for (6xy^7+cosy)dx+(2kx^2y^7-1-xsiny)dy=0 equation: 


Simplifying
(6xy7 + cosy) * dx + (2kx2y7 + -1 + -1xsiny) * dy = 0

Reorder the terms:
(cosy + 6xy7) * dx + (2kx2y7 + -1 + -1xsiny) * dy = 0

Reorder the terms for easier multiplication:
dx(cosy + 6xy7) + (2kx2y7 + -1 + -1xsiny) * dy = 0
(cosy * dx + 6xy7 * dx) + (2kx2y7 + -1 + -1xsiny) * dy = 0
(cdosxy + 6dx2y7) + (2kx2y7 + -1 + -1xsiny) * dy = 0

Reorder the terms:
cdosxy + 6dx2y7 + (-1 + -1insxy + 2kx2y7) * dy = 0

Reorder the terms for easier multiplication:
cdosxy + 6dx2y7 + dy(-1 + -1insxy + 2kx2y7) = 0
cdosxy + 6dx2y7 + (-1 * dy + -1insxy * dy + 2kx2y7 * dy) = 0

Reorder the terms:
cdosxy + 6dx2y7 + (-1dinsxy2 + 2dkx2y8 + -1dy) = 0
cdosxy + 6dx2y7 + (-1dinsxy2 + 2dkx2y8 + -1dy) = 0

Reorder the terms:
cdosxy + -1dinsxy2 + 2dkx2y8 + 6dx2y7 + -1dy = 0

Solving
cdosxy + -1dinsxy2 + 2dkx2y8 + 6dx2y7 + -1dy = 0

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add 'dinsxy2' to each side of the equation.
cdosxy + -1dinsxy2 + 2dkx2y8 + 6dx2y7 + dinsxy2 + -1dy = 0 + dinsxy2

Reorder the terms:
cdosxy + -1dinsxy2 + dinsxy2 + 2dkx2y8 + 6dx2y7 + -1dy = 0 + dinsxy2

Combine like terms: -1dinsxy2 + dinsxy2 = 0
cdosxy + 0 + 2dkx2y8 + 6dx2y7 + -1dy = 0 + dinsxy2
cdosxy + 2dkx2y8 + 6dx2y7 + -1dy = 0 + dinsxy2
Remove the zero:
cdosxy + 2dkx2y8 + 6dx2y7 + -1dy = dinsxy2

Add '-2dkx2y8' to each side of the equation.
cdosxy + 2dkx2y8 + 6dx2y7 + -2dkx2y8 + -1dy = dinsxy2 + -2dkx2y8

Reorder the terms:
cdosxy + 2dkx2y8 + -2dkx2y8 + 6dx2y7 + -1dy = dinsxy2 + -2dkx2y8

Combine like terms: 2dkx2y8 + -2dkx2y8 = 0
cdosxy + 0 + 6dx2y7 + -1dy = dinsxy2 + -2dkx2y8
cdosxy + 6dx2y7 + -1dy = dinsxy2 + -2dkx2y8

Add '-6dx2y7' to each side of the equation.
cdosxy + 6dx2y7 + -6dx2y7 + -1dy = dinsxy2 + -2dkx2y8 + -6dx2y7

Combine like terms: 6dx2y7 + -6dx2y7 = 0
cdosxy + 0 + -1dy = dinsxy2 + -2dkx2y8 + -6dx2y7
cdosxy + -1dy = dinsxy2 + -2dkx2y8 + -6dx2y7

Add 'dy' to each side of the equation.
cdosxy + -1dy + dy = dinsxy2 + -2dkx2y8 + -6dx2y7 + dy

Combine like terms: -1dy + dy = 0
cdosxy + 0 = dinsxy2 + -2dkx2y8 + -6dx2y7 + dy
cdosxy = dinsxy2 + -2dkx2y8 + -6dx2y7 + dy

Divide each side by 'dosxy'.
c = ino-1y + -2ko-1s-1xy7 + -6o-1s-1xy6 + o-1s-1x-1

Simplifying
c = ino-1y + -2ko-1s-1xy7 + -6o-1s-1xy6 + o-1s-1x-1

Reorder the terms:
c = ino-1y + -2ko-1s-1xy7 + o-1s-1x-1 + -6o-1s-1xy6

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