(5y^4+2(x^3)y)dx-(4xy^3+x^4)dy=0

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Solution for (5y^4+2(x^3)y)dx-(4xy^3+x^4)dy=0 equation: 


Simplifying
(5y4 + 2(x3) * y) * dx + -1(4xy3 + x4) * dy = 0

Multiply x3 * y
(5y4 + 2x3y) * dx + -1(4xy3 + x4) * dy = 0

Reorder the terms:
(2x3y + 5y4) * dx + -1(4xy3 + x4) * dy = 0

Reorder the terms for easier multiplication:
dx(2x3y + 5y4) + -1(4xy3 + x4) * dy = 0
(2x3y * dx + 5y4 * dx) + -1(4xy3 + x4) * dy = 0

Reorder the terms:
(5dxy4 + 2dx4y) + -1(4xy3 + x4) * dy = 0
(5dxy4 + 2dx4y) + -1(4xy3 + x4) * dy = 0

Reorder the terms for easier multiplication:
5dxy4 + 2dx4y + -1dy(4xy3 + x4) = 0
5dxy4 + 2dx4y + (4xy3 * -1dy + x4 * -1dy) = 0
5dxy4 + 2dx4y + (-4dxy4 + -1dx4y) = 0

Reorder the terms:
5dxy4 + -4dxy4 + 2dx4y + -1dx4y = 0

Combine like terms: 5dxy4 + -4dxy4 = 1dxy4
1dxy4 + 2dx4y + -1dx4y = 0

Combine like terms: 2dx4y + -1dx4y = 1dx4y
1dxy4 + 1dx4y = 0

Solving
1dxy4 + 1dx4y = 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(y3 + x3) = 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 '(y3 + x3)' equal to zero and attempt to solve:

Simplifying
y3 + x3 = 0

Reorder the terms:
x3 + y3 = 0

Solving
x3 + y3 = 0

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

Add '-1x3' to each side of the equation.
x3 + -1x3 + y3 = 0 + -1x3

Combine like terms: x3 + -1x3 = 0
0 + y3 = 0 + -1x3
y3 = 0 + -1x3
Remove the zero:
y3 = -1x3

Add '-1y3' to each side of the equation.
y3 + -1y3 = -1x3 + -1y3

Combine like terms: y3 + -1y3 = 0
0 = -1x3 + -1y3

Simplifying
0 = -1x3 + -1y3

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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