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

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


Simplifying
(x2 + 2x + y) * dx = (x + -3x2y) * dy

Reorder the terms:
(2x + x2 + y) * dx = (x + -3x2y) * dy

Reorder the terms for easier multiplication:
dx(2x + x2 + y) = (x + -3x2y) * dy
(2x * dx + x2 * dx + y * dx) = (x + -3x2y) * dy

Reorder the terms:
(dxy + 2dx2 + dx3) = (x + -3x2y) * dy
(dxy + 2dx2 + dx3) = (x + -3x2y) * dy

Reorder the terms for easier multiplication:
dxy + 2dx2 + dx3 = dy(x + -3x2y)
dxy + 2dx2 + dx3 = (x * dy + -3x2y * dy)
dxy + 2dx2 + dx3 = (dxy + -3dx2y2)

Add '-1dxy' to each side of the equation.
dxy + 2dx2 + -1dxy + dx3 = dxy + -1dxy + -3dx2y2

Reorder the terms:
dxy + -1dxy + 2dx2 + dx3 = dxy + -1dxy + -3dx2y2

Combine like terms: dxy + -1dxy = 0
0 + 2dx2 + dx3 = dxy + -1dxy + -3dx2y2
2dx2 + dx3 = dxy + -1dxy + -3dx2y2

Combine like terms: dxy + -1dxy = 0
2dx2 + dx3 = 0 + -3dx2y2
2dx2 + dx3 = -3dx2y2

Solving
2dx2 + dx3 = -3dx2y2

Solving for variable 'd'.

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

Add '3dx2y2' to each side of the equation.
2dx2 + 3dx2y2 + dx3 = -3dx2y2 + 3dx2y2

Combine like terms: -3dx2y2 + 3dx2y2 = 0
2dx2 + 3dx2y2 + dx3 = 0

Factor out the Greatest Common Factor (GCF), 'dx2'.
dx2(2 + 3y2 + 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 '(2 + 3y2 + x)' equal to zero and attempt to solve:

Simplifying
2 + 3y2 + x = 0

Reorder the terms:
2 + x + 3y2 = 0

Solving
2 + x + 3y2 = 0

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

Add '-2' to each side of the equation.
2 + x + -2 + 3y2 = 0 + -2

Reorder the terms:
2 + -2 + x + 3y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x + 3y2 = 0 + -2
x + 3y2 = 0 + -2

Combine like terms: 0 + -2 = -2
x + 3y2 = -2

Add '-1x' to each side of the equation.
x + -1x + 3y2 = -2 + -1x

Combine like terms: x + -1x = 0
0 + 3y2 = -2 + -1x
3y2 = -2 + -1x

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -2 + -1x + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -2 + -1x + -3y2

Simplifying
0 = -2 + -1x + -3y2

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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