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

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


Simplifying
(3x2 + y) * dx + (x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + y) + (x + 2y) * dy = 0
(3x2 * dx + y * dx) + (x + 2y) * dy = 0

Reorder the terms:
(dxy + 3dx3) + (x + 2y) * dy = 0
(dxy + 3dx3) + (x + 2y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 3dx3 + dy(x + 2y) = 0
dxy + 3dx3 + (x * dy + 2y * dy) = 0
dxy + 3dx3 + (dxy + 2dy2) = 0

Reorder the terms:
dxy + dxy + 3dx3 + 2dy2 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + 3dx3 + 2dy2 = 0

Solving
2dxy + 3dx3 + 2dy2 = 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 + 3x3 + 2y2) = 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 + 3x3 + 2y2)' equal to zero and attempt to solve:

Simplifying
2xy + 3x3 + 2y2 = 0

Solving
2xy + 3x3 + 2y2 = 0

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

Add '-2xy' to each side of the equation.
2xy + 3x3 + -2xy + 2y2 = 0 + -2xy

Reorder the terms:
2xy + -2xy + 3x3 + 2y2 = 0 + -2xy

Combine like terms: 2xy + -2xy = 0
0 + 3x3 + 2y2 = 0 + -2xy
3x3 + 2y2 = 0 + -2xy
Remove the zero:
3x3 + 2y2 = -2xy

Add '-3x3' to each side of the equation.
3x3 + -3x3 + 2y2 = -2xy + -3x3

Combine like terms: 3x3 + -3x3 = 0
0 + 2y2 = -2xy + -3x3
2y2 = -2xy + -3x3

Add '-2y2' to each side of the equation.
2y2 + -2y2 = -2xy + -3x3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
0 = -2xy + -3x3 + -2y2

Simplifying
0 = -2xy + -3x3 + -2y2

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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