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

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


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

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

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

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

Multiply (2x2 + y) * (-1x + x2y)
d2xy(2x2 * (-1x + x2y) + y(-1x + x2y)) = 0
d2xy((-1x * 2x2 + x2y * 2x2) + y(-1x + x2y)) = 0
d2xy((-2x3 + 2x4y) + y(-1x + x2y)) = 0
d2xy(-2x3 + 2x4y + (-1x * y + x2y * y)) = 0
d2xy(-2x3 + 2x4y + (-1xy + x2y2)) = 0

Reorder the terms:
d2xy(-1xy + x2y2 + -2x3 + 2x4y) = 0
d2xy(-1xy + x2y2 + -2x3 + 2x4y) = 0
(-1xy * d2xy + x2y2 * d2xy + -2x3 * d2xy + 2x4y * d2xy) = 0
(-1d2x2y2 + d2x3y3 + -2d2x4y + 2d2x5y2) = 0

Solving
-1d2x2y2 + d2x3y3 + -2d2x4y + 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), 'd2x2y'.
d2x2y(-1y + xy2 + -2x2 + 2x3y) = 0


Subproblem 1
Set the factor 'd2x2y' equal to zero and attempt to solve:

Simplifying
d2x2y = 0

Solving
d2x2y = 0

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

Simplifying
d2x2y = 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 + xy2 + -2x2 + 2x3y)' equal to zero and attempt to solve:

Simplifying
-1y + xy2 + -2x2 + 2x3y = 0

Reorder the terms:
xy2 + -2x2 + 2x3y + -1y = 0

Solving
xy2 + -2x2 + 2x3y + -1y = 0

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

Add '-1xy2' to each side of the equation.
xy2 + -2x2 + 2x3y + -1xy2 + -1y = 0 + -1xy2

Reorder the terms:
xy2 + -1xy2 + -2x2 + 2x3y + -1y = 0 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + -2x2 + 2x3y + -1y = 0 + -1xy2
-2x2 + 2x3y + -1y = 0 + -1xy2
Remove the zero:
-2x2 + 2x3y + -1y = -1xy2

Add '2x2' to each side of the equation.
-2x2 + 2x3y + 2x2 + -1y = -1xy2 + 2x2

Reorder the terms:
-2x2 + 2x2 + 2x3y + -1y = -1xy2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
0 + 2x3y + -1y = -1xy2 + 2x2
2x3y + -1y = -1xy2 + 2x2

Add '-2x3y' to each side of the equation.
2x3y + -2x3y + -1y = -1xy2 + 2x2 + -2x3y

Combine like terms: 2x3y + -2x3y = 0
0 + -1y = -1xy2 + 2x2 + -2x3y
-1y = -1xy2 + 2x2 + -2x3y

Add 'y' to each side of the equation.
-1y + y = -1xy2 + 2x2 + -2x3y + y

Combine like terms: -1y + y = 0
0 = -1xy2 + 2x2 + -2x3y + y

Simplifying
0 = -1xy2 + 2x2 + -2x3y + 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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