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

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


Simplifying
(2xy + y4) * dx + (3x2 + 6xy3) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + y4) + (3x2 + 6xy3) * dy = 0
(2xy * dx + y4 * dx) + (3x2 + 6xy3) * dy = 0

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

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

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

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

Combine like terms: dxy4 + 6dxy4 = 7dxy4
7dxy4 + 2dx2y + 3dx2y = 0

Combine like terms: 2dx2y + 3dx2y = 5dx2y
7dxy4 + 5dx2y = 0

Solving
7dxy4 + 5dx2y = 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), 'dxy'.
dxy(7y3 + 5x) = 0


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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(7y3 + 5x)' equal to zero and attempt to solve:

Simplifying
7y3 + 5x = 0

Reorder the terms:
5x + 7y3 = 0

Solving
5x + 7y3 = 0

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

Add '-5x' to each side of the equation.
5x + -5x + 7y3 = 0 + -5x

Combine like terms: 5x + -5x = 0
0 + 7y3 = 0 + -5x
7y3 = 0 + -5x
Remove the zero:
7y3 = -5x

Add '-7y3' to each side of the equation.
7y3 + -7y3 = -5x + -7y3

Combine like terms: 7y3 + -7y3 = 0
0 = -5x + -7y3

Simplifying
0 = -5x + -7y3

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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