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

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


Simplifying
Y2dx + (x2 + 3xy + 4y2) * dy = 0

Reorder the terms:
dxY2 + (3xy + x2 + 4y2) * dy = 0

Reorder the terms for easier multiplication:
dxY2 + dy(3xy + x2 + 4y2) = 0
dxY2 + (3xy * dy + x2 * dy + 4y2 * dy) = 0
dxY2 + (3dxy2 + dx2y + 4dy3) = 0

Solving
dxY2 + 3dxy2 + dx2y + 4dy3 = 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(xY2 + 3xy2 + x2y + 4y3) = 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 '(xY2 + 3xy2 + x2y + 4y3)' equal to zero and attempt to solve:

Simplifying
xY2 + 3xy2 + x2y + 4y3 = 0

Solving
xY2 + 3xy2 + x2y + 4y3 = 0

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

Add '-1xY2' to each side of the equation.
xY2 + 3xy2 + x2y + -1xY2 + 4y3 = 0 + -1xY2

Reorder the terms:
xY2 + -1xY2 + 3xy2 + x2y + 4y3 = 0 + -1xY2

Combine like terms: xY2 + -1xY2 = 0
0 + 3xy2 + x2y + 4y3 = 0 + -1xY2
3xy2 + x2y + 4y3 = 0 + -1xY2
Remove the zero:
3xy2 + x2y + 4y3 = -1xY2

Add '-3xy2' to each side of the equation.
3xy2 + x2y + -3xy2 + 4y3 = -1xY2 + -3xy2

Reorder the terms:
3xy2 + -3xy2 + x2y + 4y3 = -1xY2 + -3xy2

Combine like terms: 3xy2 + -3xy2 = 0
0 + x2y + 4y3 = -1xY2 + -3xy2
x2y + 4y3 = -1xY2 + -3xy2

Add '-1x2y' to each side of the equation.
x2y + -1x2y + 4y3 = -1xY2 + -3xy2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + 4y3 = -1xY2 + -3xy2 + -1x2y
4y3 = -1xY2 + -3xy2 + -1x2y

Add '-4y3' to each side of the equation.
4y3 + -4y3 = -1xY2 + -3xy2 + -1x2y + -4y3

Combine like terms: 4y3 + -4y3 = 0
0 = -1xY2 + -3xy2 + -1x2y + -4y3

Simplifying
0 = -1xY2 + -3xy2 + -1x2y + -4y3

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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