3ydx+(xy+5x)dy=0

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Solution for 3ydx+(xy+5x)dy=0 equation: 


Simplifying
3ydx + (xy + 5x) * dy = 0

Reorder the terms:
3dxy + (5x + xy) * dy = 0

Reorder the terms for easier multiplication:
3dxy + dy(5x + xy) = 0
3dxy + (5x * dy + xy * dy) = 0
3dxy + (5dxy + dxy2) = 0

Combine like terms: 3dxy + 5dxy = 8dxy
8dxy + dxy2 = 0

Solving
8dxy + dxy2 = 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(8 + y) = 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 '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Add '-1y' to each side of the equation.
y + -1y = -8 + -1y

Combine like terms: y + -1y = 0
0 = -8 + -1y

Simplifying
0 = -8 + -1y

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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