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

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


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

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

Reorder the terms:
(dxy + 3dx3) + ((x2) * y + x) * dy = 0
(dxy + 3dx3) + ((x2) * y + x) * dy = 0

Multiply x2 * y
dxy + 3dx3 + (x2y + x) * dy = 0

Reorder the terms:
dxy + 3dx3 + (x + x2y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 3dx3 + dy(x + x2y) = 0
dxy + 3dx3 + (x * dy + x2y * dy) = 0
dxy + 3dx3 + (dxy + dx2y2) = 0

Reorder the terms:
dxy + dxy + dx2y2 + 3dx3 = 0

Combine like terms: dxy + dxy = 2dxy
2dxy + dx2y2 + 3dx3 = 0

Solving
2dxy + dx2y2 + 3dx3 = 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), 'dx'.
dx(2y + xy2 + 3x2) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2y + xy2 + 3x2)' equal to zero and attempt to solve:

Simplifying
2y + xy2 + 3x2 = 0

Reorder the terms:
xy2 + 3x2 + 2y = 0

Solving
xy2 + 3x2 + 2y = 0

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

Add '-1xy2' to each side of the equation.
xy2 + 3x2 + -1xy2 + 2y = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + 3x2 + 2y = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + 3x2 + 2y = 0 + -1xy2
3x2 + 2y = 0 + -1xy2
Remove the zero:
3x2 + 2y = -1xy2

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 2y = -1xy2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 2y = -1xy2 + -3x2
2y = -1xy2 + -3x2

Add '-2y' to each side of the equation.
2y + -2y = -1xy2 + -3x2 + -2y

Combine like terms: 2y + -2y = 0
0 = -1xy2 + -3x2 + -2y

Simplifying
0 = -1xy2 + -3x2 + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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