Y(dx+y)dx-2(x^2-y)dy=0

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


Simplifying
Y(dx + y) * dx + -2(x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
Y * dx(dx + y) + -2(x2 + -1y) * dy = 0

Multiply Y * dx
dxY(dx + y) + -2(x2 + -1y) * dy = 0
(dx * dxY + y * dxY) + -2(x2 + -1y) * dy = 0

Reorder the terms:
(dxyY + d2x2Y) + -2(x2 + -1y) * dy = 0
(dxyY + d2x2Y) + -2(x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
dxyY + d2x2Y + -2dy(x2 + -1y) = 0
dxyY + d2x2Y + (x2 * -2dy + -1y * -2dy) = 0
dxyY + d2x2Y + (-2dx2y + 2dy2) = 0

Reorder the terms:
dxyY + -2dx2y + 2dy2 + d2x2Y = 0

Solving
dxyY + -2dx2y + 2dy2 + d2x2Y = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'd'.
d(xyY + -2x2y + 2y2 + dx2Y) = 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 '(xyY + -2x2y + 2y2 + dx2Y)' equal to zero and attempt to solve:

Simplifying
xyY + -2x2y + 2y2 + dx2Y = 0

Reorder the terms:
dx2Y + xyY + -2x2y + 2y2 = 0

Solving
dx2Y + xyY + -2x2y + 2y2 = 0

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

Add '-1xyY' to each side of the equation.
dx2Y + xyY + -2x2y + -1xyY + 2y2 = 0 + -1xyY

Reorder the terms:
dx2Y + xyY + -1xyY + -2x2y + 2y2 = 0 + -1xyY

Combine like terms: xyY + -1xyY = 0
dx2Y + 0 + -2x2y + 2y2 = 0 + -1xyY
dx2Y + -2x2y + 2y2 = 0 + -1xyY
Remove the zero:
dx2Y + -2x2y + 2y2 = -1xyY

Add '2x2y' to each side of the equation.
dx2Y + -2x2y + 2x2y + 2y2 = -1xyY + 2x2y

Combine like terms: -2x2y + 2x2y = 0
dx2Y + 0 + 2y2 = -1xyY + 2x2y
dx2Y + 2y2 = -1xyY + 2x2y

Add '-2y2' to each side of the equation.
dx2Y + 2y2 + -2y2 = -1xyY + 2x2y + -2y2

Combine like terms: 2y2 + -2y2 = 0
dx2Y + 0 = -1xyY + 2x2y + -2y2
dx2Y = -1xyY + 2x2y + -2y2

Divide each side by 'x2Y'.
d = -1x-1y + 2yY-1 + -2x-2y2Y-1

Simplifying
d = -1x-1y + 2yY-1 + -2x-2y2Y-1

Reorder the terms:
d = -2x-2y2Y-1 + -1x-1y + 2yY-1
Solution
d = {0, -2x-2y2Y-1 + -1x-1y + 2yY-1}

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