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

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


Simplifying
(x2 + 2y2 + 3xy) * dx + x(x + -2y) * dy = 0

Reorder the terms:
(3xy + x2 + 2y2) * dx + x(x + -2y) * dy = 0

Reorder the terms for easier multiplication:
dx(3xy + x2 + 2y2) + x(x + -2y) * dy = 0
(3xy * dx + x2 * dx + 2y2 * dx) + x(x + -2y) * dy = 0

Reorder the terms:
(2dxy2 + 3dx2y + dx3) + x(x + -2y) * dy = 0
(2dxy2 + 3dx2y + dx3) + x(x + -2y) * dy = 0

Reorder the terms for easier multiplication:
2dxy2 + 3dx2y + dx3 + x * dy(x + -2y) = 0

Multiply x * dy
2dxy2 + 3dx2y + dx3 + dxy(x + -2y) = 0
2dxy2 + 3dx2y + dx3 + (x * dxy + -2y * dxy) = 0

Reorder the terms:
2dxy2 + 3dx2y + dx3 + (-2dxy2 + dx2y) = 0
2dxy2 + 3dx2y + dx3 + (-2dxy2 + dx2y) = 0

Reorder the terms:
2dxy2 + -2dxy2 + 3dx2y + dx2y + dx3 = 0

Combine like terms: 2dxy2 + -2dxy2 = 0
0 + 3dx2y + dx2y + dx3 = 0
3dx2y + dx2y + dx3 = 0

Combine like terms: 3dx2y + dx2y = 4dx2y
4dx2y + dx3 = 0

Solving
4dx2y + dx3 = 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), 'dx2'.
dx2(4y + x) = 0


Subproblem 1
Set the factor 'dx2' equal to zero and attempt to solve:

Simplifying
dx2 = 0

Solving
dx2 = 0

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

Simplifying
dx2 = 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 '(4y + x)' equal to zero and attempt to solve:

Simplifying
4y + x = 0

Reorder the terms:
x + 4y = 0

Solving
x + 4y = 0

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

Add '-1x' to each side of the equation.
x + -1x + 4y = 0 + -1x

Combine like terms: x + -1x = 0
0 + 4y = 0 + -1x
4y = 0 + -1x
Remove the zero:
4y = -1x

Add '-4y' to each side of the equation.
4y + -4y = -1x + -4y

Combine like terms: 4y + -4y = 0
0 = -1x + -4y

Simplifying
0 = -1x + -4y

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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