(2xy+x^4)dx+(3x^2+6xy^3)dy=0

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Solution for (2xy+x^4)dx+(3x^2+6xy^3)dy=0 equation: 


Simplifying
(2xy + x4) * dx + (3x2 + 6xy3) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + x4) + (3x2 + 6xy3) * dy = 0
(2xy * dx + x4 * dx) + (3x2 + 6xy3) * dy = 0
(2dx2y + dx5) + (3x2 + 6xy3) * dy = 0

Reorder the terms:
2dx2y + dx5 + (6xy3 + 3x2) * dy = 0

Reorder the terms for easier multiplication:
2dx2y + dx5 + dy(6xy3 + 3x2) = 0
2dx2y + dx5 + (6xy3 * dy + 3x2 * dy) = 0
2dx2y + dx5 + (6dxy4 + 3dx2y) = 0

Reorder the terms:
6dxy4 + 2dx2y + 3dx2y + dx5 = 0

Combine like terms: 2dx2y + 3dx2y = 5dx2y
6dxy4 + 5dx2y + dx5 = 0

Solving
6dxy4 + 5dx2y + dx5 = 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(6y4 + 5xy + x4) = 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 '(6y4 + 5xy + x4)' equal to zero and attempt to solve:

Simplifying
6y4 + 5xy + x4 = 0

Reorder the terms:
5xy + x4 + 6y4 = 0

Solving
5xy + x4 + 6y4 = 0

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

Add '-5xy' to each side of the equation.
5xy + x4 + -5xy + 6y4 = 0 + -5xy

Reorder the terms:
5xy + -5xy + x4 + 6y4 = 0 + -5xy

Combine like terms: 5xy + -5xy = 0
0 + x4 + 6y4 = 0 + -5xy
x4 + 6y4 = 0 + -5xy
Remove the zero:
x4 + 6y4 = -5xy

Add '-1x4' to each side of the equation.
x4 + -1x4 + 6y4 = -5xy + -1x4

Combine like terms: x4 + -1x4 = 0
0 + 6y4 = -5xy + -1x4
6y4 = -5xy + -1x4

Add '-6y4' to each side of the equation.
6y4 + -6y4 = -5xy + -1x4 + -6y4

Combine like terms: 6y4 + -6y4 = 0
0 = -5xy + -1x4 + -6y4

Simplifying
0 = -5xy + -1x4 + -6y4

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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