(2x^2y+y^2)dy=(-4xy-1)dx

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Solution for (2x^2y+y^2)dy=(-4xy-1)dx equation: 


Simplifying
(2x2y + y2) * dy = (-4xy + -1) * dx

Reorder the terms for easier multiplication:
dy(2x2y + y2) = (-4xy + -1) * dx
(2x2y * dy + y2 * dy) = (-4xy + -1) * dx
(2dx2y2 + dy3) = (-4xy + -1) * dx

Reorder the terms:
2dx2y2 + dy3 = (-1 + -4xy) * dx

Reorder the terms for easier multiplication:
2dx2y2 + dy3 = dx(-1 + -4xy)
2dx2y2 + dy3 = (-1 * dx + -4xy * dx)
2dx2y2 + dy3 = (-1dx + -4dx2y)

Solving
2dx2y2 + dy3 = -1dx + -4dx2y

Solving for variable 'd'.

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

Add 'dx' to each side of the equation.
2dx2y2 + dx + dy3 = -1dx + dx + -4dx2y

Reorder the terms:
dx + 2dx2y2 + dy3 = -1dx + dx + -4dx2y

Combine like terms: -1dx + dx = 0
dx + 2dx2y2 + dy3 = 0 + -4dx2y
dx + 2dx2y2 + dy3 = -4dx2y

Add '4dx2y' to each side of the equation.
dx + 2dx2y2 + 4dx2y + dy3 = -4dx2y + 4dx2y

Reorder the terms:
dx + 4dx2y + 2dx2y2 + dy3 = -4dx2y + 4dx2y

Combine like terms: -4dx2y + 4dx2y = 0
dx + 4dx2y + 2dx2y2 + dy3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(x + 4x2y + 2x2y2 + 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 '(x + 4x2y + 2x2y2 + y3)' equal to zero and attempt to solve:

Simplifying
x + 4x2y + 2x2y2 + y3 = 0

Solving
x + 4x2y + 2x2y2 + y3 = 0

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

Add '-1x' to each side of the equation.
x + 4x2y + 2x2y2 + -1x + y3 = 0 + -1x

Reorder the terms:
x + -1x + 4x2y + 2x2y2 + y3 = 0 + -1x

Combine like terms: x + -1x = 0
0 + 4x2y + 2x2y2 + y3 = 0 + -1x
4x2y + 2x2y2 + y3 = 0 + -1x
Remove the zero:
4x2y + 2x2y2 + y3 = -1x

Add '-4x2y' to each side of the equation.
4x2y + 2x2y2 + -4x2y + y3 = -1x + -4x2y

Reorder the terms:
4x2y + -4x2y + 2x2y2 + y3 = -1x + -4x2y

Combine like terms: 4x2y + -4x2y = 0
0 + 2x2y2 + y3 = -1x + -4x2y
2x2y2 + y3 = -1x + -4x2y

Add '-2x2y2' to each side of the equation.
2x2y2 + -2x2y2 + y3 = -1x + -4x2y + -2x2y2

Combine like terms: 2x2y2 + -2x2y2 = 0
0 + y3 = -1x + -4x2y + -2x2y2
y3 = -1x + -4x2y + -2x2y2

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1x + -4x2y + -2x2y2 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1x + -4x2y + -2x2y2 + -1y3

Simplifying
0 = -1x + -4x2y + -2x2y2 + -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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