(2xy+1)dx+(x^2+4y)dy=0

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


Simplifying
(2xy + 1) * dx + (x2 + 4y) * dy = 0

Reorder the terms:
(1 + 2xy) * dx + (x2 + 4y) * dy = 0

Reorder the terms for easier multiplication:
dx(1 + 2xy) + (x2 + 4y) * dy = 0
(1 * dx + 2xy * dx) + (x2 + 4y) * dy = 0
(1dx + 2dx2y) + (x2 + 4y) * dy = 0

Reorder the terms for easier multiplication:
1dx + 2dx2y + dy(x2 + 4y) = 0
1dx + 2dx2y + (x2 * dy + 4y * dy) = 0
1dx + 2dx2y + (dx2y + 4dy2) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
1dx + 3dx2y + 4dy2 = 0

Solving
1dx + 3dx2y + 4dy2 = 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(x + 3x2y + 4y2) = 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 '(x + 3x2y + 4y2)' equal to zero and attempt to solve:

Simplifying
x + 3x2y + 4y2 = 0

Solving
x + 3x2y + 4y2 = 0

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

Add '-1x' to each side of the equation.
x + 3x2y + -1x + 4y2 = 0 + -1x

Reorder the terms:
x + -1x + 3x2y + 4y2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 3x2y + 4y2 = 0 + -1x
3x2y + 4y2 = 0 + -1x
Remove the zero:
3x2y + 4y2 = -1x

Add '-3x2y' to each side of the equation.
3x2y + -3x2y + 4y2 = -1x + -3x2y

Combine like terms: 3x2y + -3x2y = 0
0 + 4y2 = -1x + -3x2y
4y2 = -1x + -3x2y

Add '-4y2' to each side of the equation.
4y2 + -4y2 = -1x + -3x2y + -4y2

Combine like terms: 4y2 + -4y2 = 0
0 = -1x + -3x2y + -4y2

Simplifying
0 = -1x + -3x2y + -4y2

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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