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

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


Simplifying
(2y3) * dx + (2x3 + -3xy5) * dy = 0

Remove parenthesis around (2y3)
2y3 * dx + (2x3 + -3xy5) * dy = 0

Multiply y3 * dx
2dxy3 + (2x3 + -3xy5) * dy = 0

Reorder the terms:
2dxy3 + (-3xy5 + 2x3) * dy = 0

Reorder the terms for easier multiplication:
2dxy3 + dy(-3xy5 + 2x3) = 0
2dxy3 + (-3xy5 * dy + 2x3 * dy) = 0
2dxy3 + (-3dxy6 + 2dx3y) = 0

Solving
2dxy3 + -3dxy6 + 2dx3y = 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(2y2 + -3y5 + 2x2) = 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 '(2y2 + -3y5 + 2x2)' equal to zero and attempt to solve: Simplifying 2y2 + -3y5 + 2x2 = 0 Reorder the terms: 2x2 + 2y2 + -3y5 = 0 Solving 2x2 + 2y2 + -3y5 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x2' to each side of the equation. 2x2 + 2y2 + -2x2 + -3y5 = 0 + -2x2 Reorder the terms: 2x2 + -2x2 + 2y2 + -3y5 = 0 + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 2y2 + -3y5 = 0 + -2x2 2y2 + -3y5 = 0 + -2x2 Remove the zero: 2y2 + -3y5 = -2x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 + -3y5 = -2x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 + -3y5 = -2x2 + -2y2 -3y5 = -2x2 + -2y2 Add '3y5' to each side of the equation. -3y5 + 3y5 = -2x2 + -2y2 + 3y5 Combine like terms: -3y5 + 3y5 = 0 0 = -2x2 + -2y2 + 3y5 Simplifying 0 = -2x2 + -2y2 + 3y5 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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