(3x+2y+y^2)dx+(x+4y+5y^2)dy=0

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Solution for (3x+2y+y^2)dx+(x+4y+5y^2)dy=0 equation: 


Simplifying
(3x + 2y + y2) * dx + (x + 4y + 5y2) * dy = 0

Reorder the terms for easier multiplication:
dx(3x + 2y + y2) + (x + 4y + 5y2) * dy = 0
(3x * dx + 2y * dx + y2 * dx) + (x + 4y + 5y2) * dy = 0

Reorder the terms:
(2dxy + dxy2 + 3dx2) + (x + 4y + 5y2) * dy = 0
(2dxy + dxy2 + 3dx2) + (x + 4y + 5y2) * dy = 0

Reorder the terms for easier multiplication:
2dxy + dxy2 + 3dx2 + dy(x + 4y + 5y2) = 0
2dxy + dxy2 + 3dx2 + (x * dy + 4y * dy + 5y2 * dy) = 0
2dxy + dxy2 + 3dx2 + (dxy + 4dy2 + 5dy3) = 0

Reorder the terms:
2dxy + dxy + dxy2 + 3dx2 + 4dy2 + 5dy3 = 0

Combine like terms: 2dxy + dxy = 3dxy
3dxy + dxy2 + 3dx2 + 4dy2 + 5dy3 = 0

Solving
3dxy + dxy2 + 3dx2 + 4dy2 + 5dy3 = 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), 'd'.
d(3xy + xy2 + 3x2 + 4y2 + 5y3) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(3xy + xy2 + 3x2 + 4y2 + 5y3)' equal to zero and attempt to solve:

Simplifying
3xy + xy2 + 3x2 + 4y2 + 5y3 = 0

Solving
3xy + xy2 + 3x2 + 4y2 + 5y3 = 0

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

Add '-3xy' to each side of the equation.
3xy + xy2 + 3x2 + 4y2 + -3xy + 5y3 = 0 + -3xy

Reorder the terms:
3xy + -3xy + xy2 + 3x2 + 4y2 + 5y3 = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + xy2 + 3x2 + 4y2 + 5y3 = 0 + -3xy
xy2 + 3x2 + 4y2 + 5y3 = 0 + -3xy
Remove the zero:
xy2 + 3x2 + 4y2 + 5y3 = -3xy

Add '-1xy2' to each side of the equation.
xy2 + 3x2 + 4y2 + -1xy2 + 5y3 = -3xy + -1xy2

Reorder the terms:
xy2 + -1xy2 + 3x2 + 4y2 + 5y3 = -3xy + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + 3x2 + 4y2 + 5y3 = -3xy + -1xy2
3x2 + 4y2 + 5y3 = -3xy + -1xy2

Add '-3x2' to each side of the equation.
3x2 + 4y2 + -3x2 + 5y3 = -3xy + -1xy2 + -3x2

Reorder the terms:
3x2 + -3x2 + 4y2 + 5y3 = -3xy + -1xy2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 4y2 + 5y3 = -3xy + -1xy2 + -3x2
4y2 + 5y3 = -3xy + -1xy2 + -3x2

Add '-4y2' to each side of the equation.
4y2 + -4y2 + 5y3 = -3xy + -1xy2 + -3x2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 + 5y3 = -3xy + -1xy2 + -3x2 + -4y2
5y3 = -3xy + -1xy2 + -3x2 + -4y2

Add '-5y3' to each side of the equation.
5y3 + -5y3 = -3xy + -1xy2 + -3x2 + -4y2 + -5y3

Combine like terms: 5y3 + -5y3 = 0
0 = -3xy + -1xy2 + -3x2 + -4y2 + -5y3

Simplifying
0 = -3xy + -1xy2 + -3x2 + -4y2 + -5y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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