X^2dy+(x-3xy+1)dx=0

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Solution for X^2dy+(x-3xy+1)dx=0 equation: 


Simplifying
X2dy + (x + -3xy + 1) * dx = 0

Reorder the terms:
dyX2 + (1 + x + -3xy) * dx = 0

Reorder the terms for easier multiplication:
dyX2 + dx(1 + x + -3xy) = 0
dyX2 + (1 * dx + x * dx + -3xy * dx) = 0
dyX2 + (1dx + dx2 + -3dx2y) = 0

Reorder the terms:
1dx + dx2 + -3dx2y + dyX2 = 0

Solving
1dx + dx2 + -3dx2y + dyX2 = 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(x + x2 + -3x2y + yX2) = 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 '(x + x2 + -3x2y + yX2)' equal to zero and attempt to solve:

Simplifying
x + x2 + -3x2y + yX2 = 0

Solving
x + x2 + -3x2y + yX2 = 0

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

Add '-1x' to each side of the equation.
x + x2 + -3x2y + -1x + yX2 = 0 + -1x

Reorder the terms:
x + -1x + x2 + -3x2y + yX2 = 0 + -1x

Combine like terms: x + -1x = 0
0 + x2 + -3x2y + yX2 = 0 + -1x
x2 + -3x2y + yX2 = 0 + -1x
Remove the zero:
x2 + -3x2y + yX2 = -1x

Add '-1x2' to each side of the equation.
x2 + -3x2y + -1x2 + yX2 = -1x + -1x2

Reorder the terms:
x2 + -1x2 + -3x2y + yX2 = -1x + -1x2

Combine like terms: x2 + -1x2 = 0
0 + -3x2y + yX2 = -1x + -1x2
-3x2y + yX2 = -1x + -1x2

Add '3x2y' to each side of the equation.
-3x2y + 3x2y + yX2 = -1x + -1x2 + 3x2y

Combine like terms: -3x2y + 3x2y = 0
0 + yX2 = -1x + -1x2 + 3x2y
yX2 = -1x + -1x2 + 3x2y

Add '-1yX2' to each side of the equation.
yX2 + -1yX2 = -1x + -1x2 + 3x2y + -1yX2

Combine like terms: yX2 + -1yX2 = 0
0 = -1x + -1x2 + 3x2y + -1yX2

Simplifying
0 = -1x + -1x2 + 3x2y + -1yX2

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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