(3x^2y^3-6xy^2+5y)dx+(2x^3y^2-3x^2y)dy=0

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Solution for (3x^2y^3-6xy^2+5y)dx+(2x^3y^2-3x^2y)dy=0 equation: 


Simplifying
(3x2y3 + -6xy2 + 5y) * dx + (2x3y2 + -3x2y) * dy = 0

Reorder the terms:
(-6xy2 + 3x2y3 + 5y) * dx + (2x3y2 + -3x2y) * dy = 0

Reorder the terms for easier multiplication:
dx(-6xy2 + 3x2y3 + 5y) + (2x3y2 + -3x2y) * dy = 0
(-6xy2 * dx + 3x2y3 * dx + 5y * dx) + (2x3y2 + -3x2y) * dy = 0

Reorder the terms:
(5dxy + -6dx2y2 + 3dx3y3) + (2x3y2 + -3x2y) * dy = 0
(5dxy + -6dx2y2 + 3dx3y3) + (2x3y2 + -3x2y) * dy = 0

Reorder the terms:
5dxy + -6dx2y2 + 3dx3y3 + (-3x2y + 2x3y2) * dy = 0

Reorder the terms for easier multiplication:
5dxy + -6dx2y2 + 3dx3y3 + dy(-3x2y + 2x3y2) = 0
5dxy + -6dx2y2 + 3dx3y3 + (-3x2y * dy + 2x3y2 * dy) = 0
5dxy + -6dx2y2 + 3dx3y3 + (-3dx2y2 + 2dx3y3) = 0

Reorder the terms:
5dxy + -6dx2y2 + -3dx2y2 + 3dx3y3 + 2dx3y3 = 0

Combine like terms: -6dx2y2 + -3dx2y2 = -9dx2y2
5dxy + -9dx2y2 + 3dx3y3 + 2dx3y3 = 0

Combine like terms: 3dx3y3 + 2dx3y3 = 5dx3y3
5dxy + -9dx2y2 + 5dx3y3 = 0

Solving
5dxy + -9dx2y2 + 5dx3y3 = 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), 'dxy'.
dxy(5 + -9xy + 5x2y2) = 0


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

Simplifying
dxy = 0

Solving
dxy = 0

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

Simplifying
dxy = 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 '(5 + -9xy + 5x2y2)' equal to zero and attempt to solve:

Simplifying
5 + -9xy + 5x2y2 = 0

Solving
5 + -9xy + 5x2y2 = 0

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

Add '-5' to each side of the equation.
5 + -9xy + -5 + 5x2y2 = 0 + -5

Reorder the terms:
5 + -5 + -9xy + 5x2y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9xy + 5x2y2 = 0 + -5
-9xy + 5x2y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9xy + 5x2y2 = -5

Add '9xy' to each side of the equation.
-9xy + 9xy + 5x2y2 = -5 + 9xy

Combine like terms: -9xy + 9xy = 0
0 + 5x2y2 = -5 + 9xy
5x2y2 = -5 + 9xy

Add '-5x2y2' to each side of the equation.
5x2y2 + -5x2y2 = -5 + 9xy + -5x2y2

Combine like terms: 5x2y2 + -5x2y2 = 0
0 = -5 + 9xy + -5x2y2

Simplifying
0 = -5 + 9xy + -5x2y2

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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