(y^4+2y)dx+(xy^3+2y^4-4x)dy=0

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Solution for (y^4+2y)dx+(xy^3+2y^4-4x)dy=0 equation: 


Simplifying
(y4 + 2y) * dx + (xy3 + 2y4 + -4x) * dy = 0

Reorder the terms:
(2y + y4) * dx + (xy3 + 2y4 + -4x) * dy = 0

Reorder the terms for easier multiplication:
dx(2y + y4) + (xy3 + 2y4 + -4x) * dy = 0
(2y * dx + y4 * dx) + (xy3 + 2y4 + -4x) * dy = 0
(2dxy + dxy4) + (xy3 + 2y4 + -4x) * dy = 0

Reorder the terms:
2dxy + dxy4 + (-4x + xy3 + 2y4) * dy = 0

Reorder the terms for easier multiplication:
2dxy + dxy4 + dy(-4x + xy3 + 2y4) = 0
2dxy + dxy4 + (-4x * dy + xy3 * dy + 2y4 * dy) = 0
2dxy + dxy4 + (-4dxy + dxy4 + 2dy5) = 0

Reorder the terms:
2dxy + -4dxy + dxy4 + dxy4 + 2dy5 = 0

Combine like terms: 2dxy + -4dxy = -2dxy
-2dxy + dxy4 + dxy4 + 2dy5 = 0

Combine like terms: dxy4 + dxy4 = 2dxy4
-2dxy + 2dxy4 + 2dy5 = 0

Solving
-2dxy + 2dxy4 + 2dy5 = 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), '2dy'.
2dy(-1x + xy3 + y4) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(-1x + xy3 + y4)' equal to zero and attempt to solve:

Simplifying
-1x + xy3 + y4 = 0

Solving
-1x + xy3 + y4 = 0

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

Add 'x' to each side of the equation.
-1x + xy3 + x + y4 = 0 + x

Reorder the terms:
-1x + x + xy3 + y4 = 0 + x

Combine like terms: -1x + x = 0
0 + xy3 + y4 = 0 + x
xy3 + y4 = 0 + x
Remove the zero:
xy3 + y4 = x

Add '-1xy3' to each side of the equation.
xy3 + -1xy3 + y4 = x + -1xy3

Combine like terms: xy3 + -1xy3 = 0
0 + y4 = x + -1xy3
y4 = x + -1xy3

Add '-1y4' to each side of the equation.
y4 + -1y4 = x + -1xy3 + -1y4

Combine like terms: y4 + -1y4 = 0
0 = x + -1xy3 + -1y4

Simplifying
0 = x + -1xy3 + -1y4

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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