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

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


Simplifying
(3x2y + -1xy) * dx + (2x3y2 + x3y4) * dy = 0

Reorder the terms:
(-1xy + 3x2y) * dx + (2x3y2 + x3y4) * dy = 0

Reorder the terms for easier multiplication:
dx(-1xy + 3x2y) + (2x3y2 + x3y4) * dy = 0
(-1xy * dx + 3x2y * dx) + (2x3y2 + x3y4) * dy = 0
(-1dx2y + 3dx3y) + (2x3y2 + x3y4) * dy = 0

Reorder the terms for easier multiplication:
-1dx2y + 3dx3y + dy(2x3y2 + x3y4) = 0
-1dx2y + 3dx3y + (2x3y2 * dy + x3y4 * dy) = 0
-1dx2y + 3dx3y + (2dx3y3 + dx3y5) = 0

Solving
-1dx2y + 3dx3y + 2dx3y3 + dx3y5 = 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), 'dx2y'.
dx2y(-1 + 3x + 2xy2 + xy4) = 0


Subproblem 1
Set the factor 'dx2y' equal to zero and attempt to solve:

Simplifying
dx2y = 0

Solving
dx2y = 0

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

Simplifying
dx2y = 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 '(-1 + 3x + 2xy2 + xy4)' equal to zero and attempt to solve:

Simplifying
-1 + 3x + 2xy2 + xy4 = 0

Solving
-1 + 3x + 2xy2 + xy4 = 0

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

Add '1' to each side of the equation.
-1 + 3x + 2xy2 + 1 + xy4 = 0 + 1

Reorder the terms:
-1 + 1 + 3x + 2xy2 + xy4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x + 2xy2 + xy4 = 0 + 1
3x + 2xy2 + xy4 = 0 + 1

Combine like terms: 0 + 1 = 1
3x + 2xy2 + xy4 = 1

Add '-3x' to each side of the equation.
3x + 2xy2 + -3x + xy4 = 1 + -3x

Reorder the terms:
3x + -3x + 2xy2 + xy4 = 1 + -3x

Combine like terms: 3x + -3x = 0
0 + 2xy2 + xy4 = 1 + -3x
2xy2 + xy4 = 1 + -3x

Add '-2xy2' to each side of the equation.
2xy2 + -2xy2 + xy4 = 1 + -3x + -2xy2

Combine like terms: 2xy2 + -2xy2 = 0
0 + xy4 = 1 + -3x + -2xy2
xy4 = 1 + -3x + -2xy2

Add '-1xy4' to each side of the equation.
xy4 + -1xy4 = 1 + -3x + -2xy2 + -1xy4

Combine like terms: xy4 + -1xy4 = 0
0 = 1 + -3x + -2xy2 + -1xy4

Simplifying
0 = 1 + -3x + -2xy2 + -1xy4

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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