(-1x^4-1y)dx+(-1x+1y^1)dy=0

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Solution for (-1x^4-1y)dx+(-1x+1y^1)dy=0 equation:


Simplifying
(-1x4 + -1y) * dx + (-1x + 1y) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x4 + -1y) + (-1x + 1y) * dy = 0
(-1x4 * dx + -1y * dx) + (-1x + 1y) * dy = 0

Reorder the terms:
(-1dxy + -1dx5) + (-1x + 1y) * dy = 0
(-1dxy + -1dx5) + (-1x + 1y) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + -1dx5 + dy(-1x + 1y) = 0
-1dxy + -1dx5 + (-1x * dy + 1y * dy) = 0
-1dxy + -1dx5 + (-1dxy + 1dy2) = 0

Reorder the terms:
-1dxy + -1dxy + -1dx5 + 1dy2 = 0

Combine like terms: -1dxy + -1dxy = -2dxy
-2dxy + -1dx5 + 1dy2 = 0

Solving
-2dxy + -1dx5 + 1dy2 = 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), 'd'.
d(-2xy + -1x5 + y2) = 0

Subproblem 1

Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0

Subproblem 2

Set the factor '(-2xy + -1x5 + y2)' equal to zero and attempt to solve: Simplifying -2xy + -1x5 + y2 = 0 Solving -2xy + -1x5 + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '2xy' to each side of the equation. -2xy + -1x5 + 2xy + y2 = 0 + 2xy Reorder the terms: -2xy + 2xy + -1x5 + y2 = 0 + 2xy Combine like terms: -2xy + 2xy = 0 0 + -1x5 + y2 = 0 + 2xy -1x5 + y2 = 0 + 2xy Remove the zero: -1x5 + y2 = 2xy Add 'x5' to each side of the equation. -1x5 + x5 + y2 = 2xy + x5 Combine like terms: -1x5 + x5 = 0 0 + y2 = 2xy + x5 y2 = 2xy + x5 Add '-1y2' to each side of the equation. y2 + -1y2 = 2xy + x5 + -1y2 Combine like terms: y2 + -1y2 = 0 0 = 2xy + x5 + -1y2 Simplifying 0 = 2xy + x5 + -1y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

d = {0}

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