(2x+y^3)dx+(3xy^2+5y)dy=0

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Solution for (2x+y^3)dx+(3xy^2+5y)dy=0 equation: 


Simplifying
(2x + y3) * dx + (3xy2 + 5y) * dy = 0

Reorder the terms for easier multiplication:
dx(2x + y3) + (3xy2 + 5y) * dy = 0
(2x * dx + y3 * dx) + (3xy2 + 5y) * dy = 0

Reorder the terms:
(dxy3 + 2dx2) + (3xy2 + 5y) * dy = 0
(dxy3 + 2dx2) + (3xy2 + 5y) * dy = 0

Reorder the terms for easier multiplication:
dxy3 + 2dx2 + dy(3xy2 + 5y) = 0
dxy3 + 2dx2 + (3xy2 * dy + 5y * dy) = 0
dxy3 + 2dx2 + (3dxy3 + 5dy2) = 0

Reorder the terms:
dxy3 + 3dxy3 + 2dx2 + 5dy2 = 0

Combine like terms: dxy3 + 3dxy3 = 4dxy3
4dxy3 + 2dx2 + 5dy2 = 0

Solving
4dxy3 + 2dx2 + 5dy2 = 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), 'd'.
d(4xy3 + 2x2 + 5y2) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0

Subproblem 2
Set the factor '(4xy3 + 2x2 + 5y2)' equal to zero and attempt to solve:

Simplifying
4xy3 + 2x2 + 5y2 = 0

Solving
4xy3 + 2x2 + 5y2 = 0

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

Add '-4xy3' to each side of the equation.
4xy3 + 2x2 + -4xy3 + 5y2 = 0 + -4xy3

Reorder the terms:
4xy3 + -4xy3 + 2x2 + 5y2 = 0 + -4xy3

Combine like terms: 4xy3 + -4xy3 = 0
0 + 2x2 + 5y2 = 0 + -4xy3
2x2 + 5y2 = 0 + -4xy3
Remove the zero:
2x2 + 5y2 = -4xy3

Add '-2x2' to each side of the equation.
2x2 + -2x2 + 5y2 = -4xy3 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + 5y2 = -4xy3 + -2x2
5y2 = -4xy3 + -2x2

Add '-5y2' to each side of the equation.
5y2 + -5y2 = -4xy3 + -2x2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
0 = -4xy3 + -2x2 + -5y2

Simplifying
0 = -4xy3 + -2x2 + -5y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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