(6xy^3+cos(y))dx+(2kx^2y^2-xsin(y))dy=0

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Solution for (6xy^3+cos(y))dx+(2kx^2y^2-xsin(y))dy=0 equation: 


Simplifying
(6xy3 + cos(y)) * dx + (2kx2y2 + -1xsin(y)) * dy = 0

Multiply cos * y
(6xy3 + cosy) * dx + (2kx2y2 + -1xsin(y)) * dy = 0

Reorder the terms:
(cosy + 6xy3) * dx + (2kx2y2 + -1xsin(y)) * dy = 0

Reorder the terms for easier multiplication:
dx(cosy + 6xy3) + (2kx2y2 + -1xsin(y)) * dy = 0
(cosy * dx + 6xy3 * dx) + (2kx2y2 + -1xsin(y)) * dy = 0
(cdosxy + 6dx2y3) + (2kx2y2 + -1xsin(y)) * dy = 0

Multiply insx * y
cdosxy + 6dx2y3 + (2kx2y2 + -1insxy) * dy = 0

Reorder the terms:
cdosxy + 6dx2y3 + (-1insxy + 2kx2y2) * dy = 0

Reorder the terms for easier multiplication:
cdosxy + 6dx2y3 + dy(-1insxy + 2kx2y2) = 0
cdosxy + 6dx2y3 + (-1insxy * dy + 2kx2y2 * dy) = 0
cdosxy + 6dx2y3 + (-1dinsxy2 + 2dkx2y3) = 0

Reorder the terms:
cdosxy + -1dinsxy2 + 2dkx2y3 + 6dx2y3 = 0

Solving
cdosxy + -1dinsxy2 + 2dkx2y3 + 6dx2y3 = 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 + 2dkx2y3 + dinsxy2 + 6dx2y3 = 0 + dinsxy2

Reorder the terms:
cdosxy + -1dinsxy2 + dinsxy2 + 2dkx2y3 + 6dx2y3 = 0 + dinsxy2

Combine like terms: -1dinsxy2 + dinsxy2 = 0
cdosxy + 0 + 2dkx2y3 + 6dx2y3 = 0 + dinsxy2
cdosxy + 2dkx2y3 + 6dx2y3 = 0 + dinsxy2
Remove the zero:
cdosxy + 2dkx2y3 + 6dx2y3 = dinsxy2

Add '-2dkx2y3' to each side of the equation.
cdosxy + 2dkx2y3 + -2dkx2y3 + 6dx2y3 = dinsxy2 + -2dkx2y3

Combine like terms: 2dkx2y3 + -2dkx2y3 = 0
cdosxy + 0 + 6dx2y3 = dinsxy2 + -2dkx2y3
cdosxy + 6dx2y3 = dinsxy2 + -2dkx2y3

Add '-6dx2y3' to each side of the equation.
cdosxy + 6dx2y3 + -6dx2y3 = dinsxy2 + -2dkx2y3 + -6dx2y3

Combine like terms: 6dx2y3 + -6dx2y3 = 0
cdosxy + 0 = dinsxy2 + -2dkx2y3 + -6dx2y3
cdosxy = dinsxy2 + -2dkx2y3 + -6dx2y3

Divide each side by 'dosxy'.
c = ino-1y + -2ko-1s-1xy2 + -6o-1s-1xy2

Simplifying
c = ino-1y + -2ko-1s-1xy2 + -6o-1s-1xy2

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