Y((6y^2)-x-1)dx+2xdy=0

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Solution for Y((6y^2)-x-1)dx+2xdy=0 equation:


Simplifying
Y((6y2) + -1x + -1) * dx + 2xdy = 0

Reorder the terms:
Y(-1 + -1x + (6y2)) * dx + 2xdy = 0

Reorder the terms for easier multiplication:
Y * dx(-1 + -1x + (6y2)) + 2xdy = 0

Multiply Y * dx
dxY(-1 + -1x + (6y2)) + 2xdy = 0
(-1 * dxY + -1x * dxY + (6y2) * dxY) + 2xdy = 0

Reorder the terms:
(-1dxY + 6dxy2Y + -1dx2Y) + 2xdy = 0
(-1dxY + 6dxy2Y + -1dx2Y) + 2xdy = 0

Reorder the terms:
-1dxY + 2dxy + 6dxy2Y + -1dx2Y = 0

Solving
-1dxY + 2dxy + 6dxy2Y + -1dx2Y = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'dx'.
dx(-1Y + 2y + 6y2Y + -1xY) = 0

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-1Y + 2y + 6y2Y + -1xY)' equal to zero and attempt to solve: Simplifying -1Y + 2y + 6y2Y + -1xY = 0 Reorder the terms: -1Y + -1xY + 2y + 6y2Y = 0 Solving -1Y + -1xY + 2y + 6y2Y = 0 Move all terms containing d to the left, all other terms to the right. Add 'Y' to each side of the equation. -1Y + -1xY + 2y + Y + 6y2Y = 0 + Y Reorder the terms: -1Y + Y + -1xY + 2y + 6y2Y = 0 + Y Combine like terms: -1Y + Y = 0 0 + -1xY + 2y + 6y2Y = 0 + Y -1xY + 2y + 6y2Y = 0 + Y Remove the zero: -1xY + 2y + 6y2Y = Y Add 'xY' to each side of the equation. -1xY + 2y + xY + 6y2Y = Y + xY Reorder the terms: -1xY + xY + 2y + 6y2Y = Y + xY Combine like terms: -1xY + xY = 0 0 + 2y + 6y2Y = Y + xY 2y + 6y2Y = Y + xY Add '-2y' to each side of the equation. 2y + -2y + 6y2Y = Y + xY + -2y Combine like terms: 2y + -2y = 0 0 + 6y2Y = Y + xY + -2y 6y2Y = Y + xY + -2y Add '-6y2Y' to each side of the equation. 6y2Y + -6y2Y = Y + xY + -2y + -6y2Y Combine like terms: 6y2Y + -6y2Y = 0 0 = Y + xY + -2y + -6y2Y Simplifying 0 = Y + xY + -2y + -6y2Y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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