(X^3+y^3)dx+(3xy^2)dy=0

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


Simplifying
(X3 + y3) * dx + (3xy2) * dy = 0

Reorder the terms for easier multiplication:
dx(X3 + y3) + (3xy2) * dy = 0
(X3 * dx + y3 * dx) + (3xy2) * dy = 0
(dxX3 + dxy3) + (3xy2) * dy = 0

Remove parenthesis around (3xy2)
dxX3 + dxy3 + 3xy2 * dy = 0

Multiply xy2 * dy
dxX3 + dxy3 + 3dxy3 = 0

Combine like terms: dxy3 + 3dxy3 = 4dxy3
dxX3 + 4dxy3 = 0

Solving
dxX3 + 4dxy3 = 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(X3 + 4y3) = 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 '(X3 + 4y3)' equal to zero and attempt to solve:

Simplifying
X3 + 4y3 = 0

Solving
X3 + 4y3 = 0

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

Add '-1X3' to each side of the equation.
X3 + -1X3 + 4y3 = 0 + -1X3

Combine like terms: X3 + -1X3 = 0
0 + 4y3 = 0 + -1X3
4y3 = 0 + -1X3
Remove the zero:
4y3 = -1X3

Add '-4y3' to each side of the equation.
4y3 + -4y3 = -1X3 + -4y3

Combine like terms: 4y3 + -4y3 = 0
0 = -1X3 + -4y3

Simplifying
0 = -1X3 + -4y3

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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