4ydx+3(2x-1)(dy+y^4dx)=0

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Solution for 4ydx+3(2x-1)(dy+y^4dx)=0 equation: 


Simplifying
4ydx + 3(2x + -1)(dy + y4dx) = 0

Reorder the terms:
4dxy + 3(-1 + 2x)(dy + y4dx) = 0

Reorder the terms:
4dxy + 3(-1 + 2x)(dxy4 + dy) = 0

Multiply (-1 + 2x) * (dxy4 + dy)
4dxy + 3(-1(dxy4 + dy) + 2x * (dxy4 + dy)) = 0
4dxy + 3((dxy4 * -1 + dy * -1) + 2x * (dxy4 + dy)) = 0
4dxy + 3((-1dxy4 + -1dy) + 2x * (dxy4 + dy)) = 0
4dxy + 3(-1dxy4 + -1dy + (dxy4 * 2x + dy * 2x)) = 0

Reorder the terms:
4dxy + 3(-1dxy4 + -1dy + (2dxy + 2dx2y4)) = 0
4dxy + 3(-1dxy4 + -1dy + (2dxy + 2dx2y4)) = 0

Reorder the terms:
4dxy + 3(2dxy + -1dxy4 + 2dx2y4 + -1dy) = 0
4dxy + 3(2dxy + -1dxy4 + 2dx2y4 + -1dy) = 0
4dxy + (2dxy * 3 + -1dxy4 * 3 + 2dx2y4 * 3 + -1dy * 3) = 0
4dxy + (6dxy + -3dxy4 + 6dx2y4 + -3dy) = 0

Combine like terms: 4dxy + 6dxy = 10dxy
10dxy + -3dxy4 + 6dx2y4 + -3dy = 0

Solving
10dxy + -3dxy4 + 6dx2y4 + -3dy = 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), 'dy'.
dy(10x + -3xy3 + 6x2y3 + -3) = 0


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 '(10x + -3xy3 + 6x2y3 + -3)' equal to zero and attempt to solve:

Simplifying
10x + -3xy3 + 6x2y3 + -3 = 0

Reorder the terms:
-3 + 10x + -3xy3 + 6x2y3 = 0

Solving
-3 + 10x + -3xy3 + 6x2y3 = 0

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

Add '3' to each side of the equation.
-3 + 10x + -3xy3 + 3 + 6x2y3 = 0 + 3

Reorder the terms:
-3 + 3 + 10x + -3xy3 + 6x2y3 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 10x + -3xy3 + 6x2y3 = 0 + 3
10x + -3xy3 + 6x2y3 = 0 + 3

Combine like terms: 0 + 3 = 3
10x + -3xy3 + 6x2y3 = 3

Add '-10x' to each side of the equation.
10x + -3xy3 + -10x + 6x2y3 = 3 + -10x

Reorder the terms:
10x + -10x + -3xy3 + 6x2y3 = 3 + -10x

Combine like terms: 10x + -10x = 0
0 + -3xy3 + 6x2y3 = 3 + -10x
-3xy3 + 6x2y3 = 3 + -10x

Add '3xy3' to each side of the equation.
-3xy3 + 3xy3 + 6x2y3 = 3 + -10x + 3xy3

Combine like terms: -3xy3 + 3xy3 = 0
0 + 6x2y3 = 3 + -10x + 3xy3
6x2y3 = 3 + -10x + 3xy3

Add '-6x2y3' to each side of the equation.
6x2y3 + -6x2y3 = 3 + -10x + 3xy3 + -6x2y3

Combine like terms: 6x2y3 + -6x2y3 = 0
0 = 3 + -10x + 3xy3 + -6x2y3

Simplifying
0 = 3 + -10x + 3xy3 + -6x2y3

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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