y(3x^3y^3+6)dx+x(2x^3y^3-5)dy=0

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Solution for y(3x^3y^3+6)dx+x(2x^3y^3-5)dy=0 equation:


Simplifying
y(3x3y3 + 6) * dx + x(2x3y3 + -5) * dy = 0

Reorder the terms:
y(6 + 3x3y3) * dx + x(2x3y3 + -5) * dy = 0

Reorder the terms for easier multiplication:
y * dx(6 + 3x3y3) + x(2x3y3 + -5) * dy = 0

Multiply y * dx
dxy(6 + 3x3y3) + x(2x3y3 + -5) * dy = 0
(6 * dxy + 3x3y3 * dxy) + x(2x3y3 + -5) * dy = 0
(6dxy + 3dx4y4) + x(2x3y3 + -5) * dy = 0

Reorder the terms:
6dxy + 3dx4y4 + x(-5 + 2x3y3) * dy = 0

Reorder the terms for easier multiplication:
6dxy + 3dx4y4 + x * dy(-5 + 2x3y3) = 0

Multiply x * dy
6dxy + 3dx4y4 + dxy(-5 + 2x3y3) = 0
6dxy + 3dx4y4 + (-5 * dxy + 2x3y3 * dxy) = 0
6dxy + 3dx4y4 + (-5dxy + 2dx4y4) = 0

Reorder the terms:
6dxy + -5dxy + 3dx4y4 + 2dx4y4 = 0

Combine like terms: 6dxy + -5dxy = 1dxy
1dxy + 3dx4y4 + 2dx4y4 = 0

Combine like terms: 3dx4y4 + 2dx4y4 = 5dx4y4
1dxy + 5dx4y4 = 0

Solving
1dxy + 5dx4y4 = 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(1 + 5x3y3) = 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 '(1 + 5x3y3)' equal to zero and attempt to solve: Simplifying 1 + 5x3y3 = 0 Solving 1 + 5x3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 5x3y3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x3y3 = 0 + -1 5x3y3 = 0 + -1 Combine like terms: 0 + -1 = -1 5x3y3 = -1 Add '-5x3y3' to each side of the equation. 5x3y3 + -5x3y3 = -1 + -5x3y3 Combine like terms: 5x3y3 + -5x3y3 = 0 0 = -1 + -5x3y3 Simplifying 0 = -1 + -5x3y3 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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