(4x^2+xy-3y^2)dx+(-5x^2+2xy+y^2)dy=0

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Solution for (4x^2+xy-3y^2)dx+(-5x^2+2xy+y^2)dy=0 equation: 


Simplifying
(4x2 + xy + -3y2) * dx + (-5x2 + 2xy + y2) * dy = 0

Reorder the terms:
(xy + 4x2 + -3y2) * dx + (-5x2 + 2xy + y2) * dy = 0

Reorder the terms for easier multiplication:
dx(xy + 4x2 + -3y2) + (-5x2 + 2xy + y2) * dy = 0
(xy * dx + 4x2 * dx + -3y2 * dx) + (-5x2 + 2xy + y2) * dy = 0

Reorder the terms:
(-3dxy2 + dx2y + 4dx3) + (-5x2 + 2xy + y2) * dy = 0
(-3dxy2 + dx2y + 4dx3) + (-5x2 + 2xy + y2) * dy = 0

Reorder the terms:
-3dxy2 + dx2y + 4dx3 + (2xy + -5x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
-3dxy2 + dx2y + 4dx3 + dy(2xy + -5x2 + y2) = 0
-3dxy2 + dx2y + 4dx3 + (2xy * dy + -5x2 * dy + y2 * dy) = 0
-3dxy2 + dx2y + 4dx3 + (2dxy2 + -5dx2y + dy3) = 0

Reorder the terms:
-3dxy2 + 2dxy2 + dx2y + -5dx2y + 4dx3 + dy3 = 0

Combine like terms: -3dxy2 + 2dxy2 = -1dxy2
-1dxy2 + dx2y + -5dx2y + 4dx3 + dy3 = 0

Combine like terms: dx2y + -5dx2y = -4dx2y
-1dxy2 + -4dx2y + 4dx3 + dy3 = 0

Solving
-1dxy2 + -4dx2y + 4dx3 + dy3 = 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(-1xy2 + -4x2y + 4x3 + y3) = 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 '(-1xy2 + -4x2y + 4x3 + y3)' equal to zero and attempt to solve:

Simplifying
-1xy2 + -4x2y + 4x3 + y3 = 0

Solving
-1xy2 + -4x2y + 4x3 + y3 = 0

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

Add 'xy2' to each side of the equation.
-1xy2 + -4x2y + 4x3 + xy2 + y3 = 0 + xy2

Reorder the terms:
-1xy2 + xy2 + -4x2y + 4x3 + y3 = 0 + xy2

Combine like terms: -1xy2 + xy2 = 0
0 + -4x2y + 4x3 + y3 = 0 + xy2
-4x2y + 4x3 + y3 = 0 + xy2
Remove the zero:
-4x2y + 4x3 + y3 = xy2

Add '4x2y' to each side of the equation.
-4x2y + 4x3 + 4x2y + y3 = xy2 + 4x2y

Reorder the terms:
-4x2y + 4x2y + 4x3 + y3 = xy2 + 4x2y

Combine like terms: -4x2y + 4x2y = 0
0 + 4x3 + y3 = xy2 + 4x2y
4x3 + y3 = xy2 + 4x2y

Add '-4x3' to each side of the equation.
4x3 + -4x3 + y3 = xy2 + 4x2y + -4x3

Combine like terms: 4x3 + -4x3 = 0
0 + y3 = xy2 + 4x2y + -4x3
y3 = xy2 + 4x2y + -4x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = xy2 + 4x2y + -4x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = xy2 + 4x2y + -4x3 + -1y3

Simplifying
0 = xy2 + 4x2y + -4x3 + -1y3

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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