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

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


Simplifying
(x + 4y2) * dy + (y + x2) * dx = 0

Reorder the terms for easier multiplication:
dy(x + 4y2) + (y + x2) * dx = 0
(x * dy + 4y2 * dy) + (y + x2) * dx = 0
(dxy + 4dy3) + (y + x2) * dx = 0

Reorder the terms:
dxy + 4dy3 + (x2 + y) * dx = 0

Reorder the terms for easier multiplication:
dxy + 4dy3 + dx(x2 + y) = 0
dxy + 4dy3 + (x2 * dx + y * dx) = 0

Reorder the terms:
dxy + 4dy3 + (dxy + dx3) = 0
dxy + 4dy3 + (dxy + dx3) = 0

Reorder the terms:
dxy + dxy + dx3 + 4dy3 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dx3 + 4dy3 = 0

Solving
2dxy + dx3 + 4dy3 = 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(2xy + x3 + 4y3) = 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 '(2xy + x3 + 4y3)' equal to zero and attempt to solve:

Simplifying
2xy + x3 + 4y3 = 0

Solving
2xy + x3 + 4y3 = 0

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

Add '-2xy' to each side of the equation.
2xy + x3 + -2xy + 4y3 = 0 + -2xy

Reorder the terms:
2xy + -2xy + x3 + 4y3 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + x3 + 4y3 = 0 + -2xy
x3 + 4y3 = 0 + -2xy
Remove the zero:
x3 + 4y3 = -2xy

Add '-1x3' to each side of the equation.
x3 + -1x3 + 4y3 = -2xy + -1x3

Combine like terms: x3 + -1x3 = 0
0 + 4y3 = -2xy + -1x3
4y3 = -2xy + -1x3

Add '-4y3' to each side of the equation.
4y3 + -4y3 = -2xy + -1x3 + -4y3

Combine like terms: 4y3 + -4y3 = 0
0 = -2xy + -1x3 + -4y3

Simplifying
0 = -2xy + -1x3 + -4y3

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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