2ydx+(y^2-6x)dy=0

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Solution for 2ydx+(y^2-6x)dy=0 equation: 


Simplifying
2ydx + (y2 + -6x) * dy = 0

Reorder the terms:
2dxy + (-6x + y2) * dy = 0

Reorder the terms for easier multiplication:
2dxy + dy(-6x + y2) = 0
2dxy + (-6x * dy + y2 * dy) = 0
2dxy + (-6dxy + dy3) = 0

Combine like terms: 2dxy + -6dxy = -4dxy
-4dxy + dy3 = 0

Solving
-4dxy + dy3 = 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(-4x + y2) = 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 '(-4x + y2)' equal to zero and attempt to solve:

Simplifying
-4x + y2 = 0

Solving
-4x + y2 = 0

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

Add '4x' to each side of the equation.
-4x + 4x + y2 = 0 + 4x

Combine like terms: -4x + 4x = 0
0 + y2 = 0 + 4x
y2 = 0 + 4x
Remove the zero:
y2 = 4x

Add '-1y2' to each side of the equation.
y2 + -1y2 = 4x + -1y2

Combine like terms: y2 + -1y2 = 0
0 = 4x + -1y2

Simplifying
0 = 4x + -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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