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

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


Simplifying
(4xy + 3y4) * dx + (2x2 + 5xy3) * dy = 0

Reorder the terms for easier multiplication:
dx(4xy + 3y4) + (2x2 + 5xy3) * dy = 0
(4xy * dx + 3y4 * dx) + (2x2 + 5xy3) * dy = 0

Reorder the terms:
(3dxy4 + 4dx2y) + (2x2 + 5xy3) * dy = 0
(3dxy4 + 4dx2y) + (2x2 + 5xy3) * dy = 0

Reorder the terms:
3dxy4 + 4dx2y + (5xy3 + 2x2) * dy = 0

Reorder the terms for easier multiplication:
3dxy4 + 4dx2y + dy(5xy3 + 2x2) = 0
3dxy4 + 4dx2y + (5xy3 * dy + 2x2 * dy) = 0
3dxy4 + 4dx2y + (5dxy4 + 2dx2y) = 0

Reorder the terms:
3dxy4 + 5dxy4 + 4dx2y + 2dx2y = 0

Combine like terms: 3dxy4 + 5dxy4 = 8dxy4
8dxy4 + 4dx2y + 2dx2y = 0

Combine like terms: 4dx2y + 2dx2y = 6dx2y
8dxy4 + 6dx2y = 0

Solving
8dxy4 + 6dx2y = 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), '2dxy'.
2dxy(4y3 + 3x) = 0

Ignore the factor 2.

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 '(4y3 + 3x)' equal to zero and attempt to solve: Simplifying 4y3 + 3x = 0 Reorder the terms: 3x + 4y3 = 0 Solving 3x + 4y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + -3x + 4y3 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 4y3 = 0 + -3x 4y3 = 0 + -3x Remove the zero: 4y3 = -3x Add '-4y3' to each side of the equation. 4y3 + -4y3 = -3x + -4y3 Combine like terms: 4y3 + -4y3 = 0 0 = -3x + -4y3 Simplifying 0 = -3x + -4y3 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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