(X^3-3xy^2)dx+(y^3-3x^2y)day=0

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


Simplifying
(X3 + -3xy2) * dx + (y3 + -3x2y) * day = 0

Reorder the terms for easier multiplication:
dx(X3 + -3xy2) + (y3 + -3x2y) * day = 0
(X3 * dx + -3xy2 * dx) + (y3 + -3x2y) * day = 0
(dxX3 + -3dx2y2) + (y3 + -3x2y) * day = 0

Reorder the terms:
dxX3 + -3dx2y2 + (-3x2y + y3) * day = 0

Reorder the terms for easier multiplication:
dxX3 + -3dx2y2 + ady(-3x2y + y3) = 0
dxX3 + -3dx2y2 + (-3x2y * ady + y3 * ady) = 0
dxX3 + -3dx2y2 + (-3adx2y2 + ady4) = 0

Reorder the terms:
-3adx2y2 + ady4 + dxX3 + -3dx2y2 = 0

Solving
-3adx2y2 + ady4 + dxX3 + -3dx2y2 = 0

Solving for variable 'a'.

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

Add '-1dxX3' to each side of the equation.
-3adx2y2 + ady4 + dxX3 + -1dxX3 + -3dx2y2 = 0 + -1dxX3

Combine like terms: dxX3 + -1dxX3 = 0
-3adx2y2 + ady4 + 0 + -3dx2y2 = 0 + -1dxX3
-3adx2y2 + ady4 + -3dx2y2 = 0 + -1dxX3
Remove the zero:
-3adx2y2 + ady4 + -3dx2y2 = -1dxX3

Add '3dx2y2' to each side of the equation.
-3adx2y2 + ady4 + -3dx2y2 + 3dx2y2 = -1dxX3 + 3dx2y2

Combine like terms: -3dx2y2 + 3dx2y2 = 0
-3adx2y2 + ady4 + 0 = -1dxX3 + 3dx2y2
-3adx2y2 + ady4 = -1dxX3 + 3dx2y2

Reorder the terms:
-3adx2y2 + ady4 + dxX3 + -3dx2y2 = -1dxX3 + dxX3 + 3dx2y2 + -3dx2y2

Combine like terms: -1dxX3 + dxX3 = 0
-3adx2y2 + ady4 + dxX3 + -3dx2y2 = 0 + 3dx2y2 + -3dx2y2
-3adx2y2 + ady4 + dxX3 + -3dx2y2 = 3dx2y2 + -3dx2y2

Combine like terms: 3dx2y2 + -3dx2y2 = 0
-3adx2y2 + ady4 + dxX3 + -3dx2y2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-3ax2y2 + ay4 + xX3 + -3x2y2) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Add '-1d' to each side of the equation.
d + -1d = 0 + -1d
Remove the zero:
0 = -1d

Simplifying
0 = -1d

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 '(-3ax2y2 + ay4 + xX3 + -3x2y2)' equal to zero and attempt to solve:

Simplifying
-3ax2y2 + ay4 + xX3 + -3x2y2 = 0

Solving
-3ax2y2 + ay4 + xX3 + -3x2y2 = 0

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

Add '-1xX3' to each side of the equation.
-3ax2y2 + ay4 + xX3 + -1xX3 + -3x2y2 = 0 + -1xX3

Combine like terms: xX3 + -1xX3 = 0
-3ax2y2 + ay4 + 0 + -3x2y2 = 0 + -1xX3
-3ax2y2 + ay4 + -3x2y2 = 0 + -1xX3
Remove the zero:
-3ax2y2 + ay4 + -3x2y2 = -1xX3

Add '3x2y2' to each side of the equation.
-3ax2y2 + ay4 + -3x2y2 + 3x2y2 = -1xX3 + 3x2y2

Combine like terms: -3x2y2 + 3x2y2 = 0
-3ax2y2 + ay4 + 0 = -1xX3 + 3x2y2
-3ax2y2 + ay4 = -1xX3 + 3x2y2

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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