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

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


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

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

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

Remove parenthesis around (x + 4xy + 5y2)
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = 0

Solving
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = 0

Solving for variable 'd'.

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

Add '-1x' to each side of the equation.
2dxy + dxy2 + 3dx2 + x + 4xy + -1x + 5y2 = 0 + -1x

Reorder the terms:
2dxy + dxy2 + 3dx2 + x + -1x + 4xy + 5y2 = 0 + -1x

Combine like terms: x + -1x = 0
2dxy + dxy2 + 3dx2 + 0 + 4xy + 5y2 = 0 + -1x
2dxy + dxy2 + 3dx2 + 4xy + 5y2 = 0 + -1x
Remove the zero:
2dxy + dxy2 + 3dx2 + 4xy + 5y2 = -1x

Add '-4xy' to each side of the equation.
2dxy + dxy2 + 3dx2 + 4xy + -4xy + 5y2 = -1x + -4xy

Combine like terms: 4xy + -4xy = 0
2dxy + dxy2 + 3dx2 + 0 + 5y2 = -1x + -4xy
2dxy + dxy2 + 3dx2 + 5y2 = -1x + -4xy

Add '-5y2' to each side of the equation.
2dxy + dxy2 + 3dx2 + 5y2 + -5y2 = -1x + -4xy + -5y2

Combine like terms: 5y2 + -5y2 = 0
2dxy + dxy2 + 3dx2 + 0 = -1x + -4xy + -5y2
2dxy + dxy2 + 3dx2 = -1x + -4xy + -5y2

Reorder the terms:
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = -1x + x + -4xy + 4xy + -5y2 + 5y2

Combine like terms: -1x + x = 0
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = 0 + -4xy + 4xy + -5y2 + 5y2
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = -4xy + 4xy + -5y2 + 5y2

Combine like terms: -4xy + 4xy = 0
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = 0 + -5y2 + 5y2
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = -5y2 + 5y2

Combine like terms: -5y2 + 5y2 = 0
2dxy + dxy2 + 3dx2 + x + 4xy + 5y2 = 0

The solution to this equation could not be determined.

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