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

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


Simplifying
(3x2y) * dx + (2x3 + 3y3) * dy = 0

Remove parenthesis around (3x2y)
3x2y * dx + (2x3 + 3y3) * dy = 0

Multiply x2y * dx
3dx3y + (2x3 + 3y3) * dy = 0

Reorder the terms for easier multiplication:
3dx3y + dy(2x3 + 3y3) = 0
3dx3y + (2x3 * dy + 3y3 * dy) = 0
3dx3y + (2dx3y + 3dy4) = 0

Combine like terms: 3dx3y + 2dx3y = 5dx3y
5dx3y + 3dy4 = 0

Solving
5dx3y + 3dy4 = 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), 'dy'.
dy(5x3 + 3y3) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(5x3 + 3y3)' equal to zero and attempt to solve:

Simplifying
5x3 + 3y3 = 0

Solving
5x3 + 3y3 = 0

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

Add '-5x3' to each side of the equation.
5x3 + -5x3 + 3y3 = 0 + -5x3

Combine like terms: 5x3 + -5x3 = 0
0 + 3y3 = 0 + -5x3
3y3 = 0 + -5x3
Remove the zero:
3y3 = -5x3

Add '-3y3' to each side of the equation.
3y3 + -3y3 = -5x3 + -3y3

Combine like terms: 3y3 + -3y3 = 0
0 = -5x3 + -3y3

Simplifying
0 = -5x3 + -3y3

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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