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

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


Simplifying
(2y + 3x2y3) * dx + (3x + 5x3y2) * dy = 0

Reorder the terms:
(3x2y3 + 2y) * dx + (3x + 5x3y2) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2y3 + 2y) + (3x + 5x3y2) * dy = 0
(3x2y3 * dx + 2y * dx) + (3x + 5x3y2) * dy = 0

Reorder the terms:
(2dxy + 3dx3y3) + (3x + 5x3y2) * dy = 0
(2dxy + 3dx3y3) + (3x + 5x3y2) * dy = 0

Reorder the terms for easier multiplication:
2dxy + 3dx3y3 + dy(3x + 5x3y2) = 0
2dxy + 3dx3y3 + (3x * dy + 5x3y2 * dy) = 0
2dxy + 3dx3y3 + (3dxy + 5dx3y3) = 0

Reorder the terms:
2dxy + 3dxy + 3dx3y3 + 5dx3y3 = 0

Combine like terms: 2dxy + 3dxy = 5dxy
5dxy + 3dx3y3 + 5dx3y3 = 0

Combine like terms: 3dx3y3 + 5dx3y3 = 8dx3y3
5dxy + 8dx3y3 = 0

Solving
5dxy + 8dx3y3 = 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(5 + 8x2y2) = 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 '(5 + 8x2y2)' equal to zero and attempt to solve: Simplifying 5 + 8x2y2 = 0 Solving 5 + 8x2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 8x2y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8x2y2 = 0 + -5 8x2y2 = 0 + -5 Combine like terms: 0 + -5 = -5 8x2y2 = -5 Add '-8x2y2' to each side of the equation. 8x2y2 + -8x2y2 = -5 + -8x2y2 Combine like terms: 8x2y2 + -8x2y2 = 0 0 = -5 + -8x2y2 Simplifying 0 = -5 + -8x2y2 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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