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

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


Simplifying
3((3x2) + (y2)) * dx + -1(2xy) * dy = 0
3((3x2) + y2) * dx + -1(2xy) * dy = 0

Reorder the terms for easier multiplication:
3dx((3x2) + y2) + -1(2xy) * dy = 0
((3x2) * 3dx + y2 * 3dx) + -1(2xy) * dy = 0

Reorder the terms:
(3dxy2 + 9dx3) + -1(2xy) * dy = 0
(3dxy2 + 9dx3) + -1(2xy) * dy = 0

Remove parenthesis around (2xy)
3dxy2 + 9dx3 + -1 * 2xy * dy = 0

Multiply -1 * 2
3dxy2 + 9dx3 + -2xy * dy = 0

Multiply xy * dy
3dxy2 + 9dx3 + -2dxy2 = 0

Reorder the terms:
3dxy2 + -2dxy2 + 9dx3 = 0

Combine like terms: 3dxy2 + -2dxy2 = 1dxy2
1dxy2 + 9dx3 = 0

Solving
1dxy2 + 9dx3 = 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), 'dx'.
dx(y2 + 9x2) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(y2 + 9x2)' equal to zero and attempt to solve:

Simplifying
y2 + 9x2 = 0

Reorder the terms:
9x2 + y2 = 0

Solving
9x2 + y2 = 0

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

Add '-9x2' to each side of the equation.
9x2 + -9x2 + y2 = 0 + -9x2

Combine like terms: 9x2 + -9x2 = 0
0 + y2 = 0 + -9x2
y2 = 0 + -9x2
Remove the zero:
y2 = -9x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -9x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -9x2 + -1y2

Simplifying
0 = -9x2 + -1y2

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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