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

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


Simplifying
y2dx + (x * y + 3y3) * dy = 0

Multiply x * y
dxy2 + (xy + 3y3) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + dy(xy + 3y3) = 0
dxy2 + (xy * dy + 3y3 * dy) = 0
dxy2 + (dxy2 + 3dy4) = 0

Combine like terms: dxy2 + dxy2 = 2dxy2
2dxy2 + 3dy4 = 0

Solving
2dxy2 + 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), 'dy2'.
dy2(2x + 3y2) = 0


Subproblem 1
Set the factor 'dy2' equal to zero and attempt to solve:

Simplifying
dy2 = 0

Solving
dy2 = 0

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

Simplifying
dy2 = 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 '(2x + 3y2)' equal to zero and attempt to solve:

Simplifying
2x + 3y2 = 0

Solving
2x + 3y2 = 0

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

Add '-2x' to each side of the equation.
2x + -2x + 3y2 = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + 3y2 = 0 + -2x
3y2 = 0 + -2x
Remove the zero:
3y2 = -2x

Add '-3y2' to each side of the equation.
3y2 + -3y2 = -2x + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = -2x + -3y2

Simplifying
0 = -2x + -3y2

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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