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

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


Simplifying
(2x2 + y) * dx(x2y + -1y) * dy = 0

Reorder the terms for easier multiplication:
dx * dy(2x2 + y)(x2y + -1y) = 0

Multiply dx * dy
d2xy(2x2 + y)(x2y + -1y) = 0

Multiply (2x2 + y) * (x2y + -1y)
d2xy(2x2 * (x2y + -1y) + y(x2y + -1y)) = 0
d2xy((x2y * 2x2 + -1y * 2x2) + y(x2y + -1y)) = 0

Reorder the terms:
d2xy((-2x2y + 2x4y) + y(x2y + -1y)) = 0
d2xy((-2x2y + 2x4y) + y(x2y + -1y)) = 0
d2xy(-2x2y + 2x4y + (x2y * y + -1y * y)) = 0
d2xy(-2x2y + 2x4y + (x2y2 + -1y2)) = 0

Reorder the terms:
d2xy(-2x2y + x2y2 + 2x4y + -1y2) = 0
d2xy(-2x2y + x2y2 + 2x4y + -1y2) = 0
(-2x2y * d2xy + x2y2 * d2xy + 2x4y * d2xy + -1y2 * d2xy) = 0

Reorder the terms:
(-1d2xy3 + -2d2x3y2 + d2x3y3 + 2d2x5y2) = 0
(-1d2xy3 + -2d2x3y2 + d2x3y3 + 2d2x5y2) = 0

Solving
-1d2xy3 + -2d2x3y2 + d2x3y3 + 2d2x5y2 = 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), 'd2xy2'.
d2xy2(-1y + -2x2 + x2y + 2x4) = 0


Subproblem 1
Set the factor 'd2xy2' equal to zero and attempt to solve:

Simplifying
d2xy2 = 0

Solving
d2xy2 = 0

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

Simplifying
d2xy2 = 0

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 '(-1y + -2x2 + x2y + 2x4)' equal to zero and attempt to solve:

Simplifying
-1y + -2x2 + x2y + 2x4 = 0

Reorder the terms:
-2x2 + x2y + 2x4 + -1y = 0

Solving
-2x2 + x2y + 2x4 + -1y = 0

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

Add '2x2' to each side of the equation.
-2x2 + x2y + 2x4 + 2x2 + -1y = 0 + 2x2

Reorder the terms:
-2x2 + 2x2 + x2y + 2x4 + -1y = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + x2y + 2x4 + -1y = 0 + 2x2
x2y + 2x4 + -1y = 0 + 2x2
Remove the zero:
x2y + 2x4 + -1y = 2x2

Add '-1x2y' to each side of the equation.
x2y + 2x4 + -1x2y + -1y = 2x2 + -1x2y

Reorder the terms:
x2y + -1x2y + 2x4 + -1y = 2x2 + -1x2y

Combine like terms: x2y + -1x2y = 0
0 + 2x4 + -1y = 2x2 + -1x2y
2x4 + -1y = 2x2 + -1x2y

Add '-2x4' to each side of the equation.
2x4 + -2x4 + -1y = 2x2 + -1x2y + -2x4

Combine like terms: 2x4 + -2x4 = 0
0 + -1y = 2x2 + -1x2y + -2x4
-1y = 2x2 + -1x2y + -2x4

Add 'y' to each side of the equation.
-1y + y = 2x2 + -1x2y + -2x4 + y

Combine like terms: -1y + y = 0
0 = 2x2 + -1x2y + -2x4 + y

Simplifying
0 = 2x2 + -1x2y + -2x4 + y

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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