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

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


Simplifying
(5x4 + 3x2y2 + -2xy3) * dx + (2x2y + -3x2y2 + -5y2) * dy = 0

Reorder the terms:
(-2xy3 + 3x2y2 + 5x4) * dx + (2x2y + -3x2y2 + -5y2) * dy = 0

Reorder the terms for easier multiplication:
dx(-2xy3 + 3x2y2 + 5x4) + (2x2y + -3x2y2 + -5y2) * dy = 0
(-2xy3 * dx + 3x2y2 * dx + 5x4 * dx) + (2x2y + -3x2y2 + -5y2) * dy = 0
(-2dx2y3 + 3dx3y2 + 5dx5) + (2x2y + -3x2y2 + -5y2) * dy = 0

Reorder the terms for easier multiplication:
-2dx2y3 + 3dx3y2 + 5dx5 + dy(2x2y + -3x2y2 + -5y2) = 0
-2dx2y3 + 3dx3y2 + 5dx5 + (2x2y * dy + -3x2y2 * dy + -5y2 * dy) = 0
-2dx2y3 + 3dx3y2 + 5dx5 + (2dx2y2 + -3dx2y3 + -5dy3) = 0

Reorder the terms:
2dx2y2 + -2dx2y3 + -3dx2y3 + 3dx3y2 + 5dx5 + -5dy3 = 0

Combine like terms: -2dx2y3 + -3dx2y3 = -5dx2y3
2dx2y2 + -5dx2y3 + 3dx3y2 + 5dx5 + -5dy3 = 0

Solving
2dx2y2 + -5dx2y3 + 3dx3y2 + 5dx5 + -5dy3 = 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), 'd'.
d(2x2y2 + -5x2y3 + 3x3y2 + 5x5 + -5y3) = 0

Subproblem 1

Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0

Subproblem 2

Set the factor '(2x2y2 + -5x2y3 + 3x3y2 + 5x5 + -5y3)' equal to zero and attempt to solve: Simplifying 2x2y2 + -5x2y3 + 3x3y2 + 5x5 + -5y3 = 0 Solving 2x2y2 + -5x2y3 + 3x3y2 + 5x5 + -5y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x2y2' to each side of the equation. 2x2y2 + -5x2y3 + 3x3y2 + 5x5 + -2x2y2 + -5y3 = 0 + -2x2y2 Reorder the terms: 2x2y2 + -2x2y2 + -5x2y3 + 3x3y2 + 5x5 + -5y3 = 0 + -2x2y2 Combine like terms: 2x2y2 + -2x2y2 = 0 0 + -5x2y3 + 3x3y2 + 5x5 + -5y3 = 0 + -2x2y2 -5x2y3 + 3x3y2 + 5x5 + -5y3 = 0 + -2x2y2 Remove the zero: -5x2y3 + 3x3y2 + 5x5 + -5y3 = -2x2y2 Add '5x2y3' to each side of the equation. -5x2y3 + 3x3y2 + 5x5 + 5x2y3 + -5y3 = -2x2y2 + 5x2y3 Reorder the terms: -5x2y3 + 5x2y3 + 3x3y2 + 5x5 + -5y3 = -2x2y2 + 5x2y3 Combine like terms: -5x2y3 + 5x2y3 = 0 0 + 3x3y2 + 5x5 + -5y3 = -2x2y2 + 5x2y3 3x3y2 + 5x5 + -5y3 = -2x2y2 + 5x2y3 Add '-3x3y2' to each side of the equation. 3x3y2 + 5x5 + -3x3y2 + -5y3 = -2x2y2 + 5x2y3 + -3x3y2 Reorder the terms: 3x3y2 + -3x3y2 + 5x5 + -5y3 = -2x2y2 + 5x2y3 + -3x3y2 Combine like terms: 3x3y2 + -3x3y2 = 0 0 + 5x5 + -5y3 = -2x2y2 + 5x2y3 + -3x3y2 5x5 + -5y3 = -2x2y2 + 5x2y3 + -3x3y2 Add '-5x5' to each side of the equation. 5x5 + -5x5 + -5y3 = -2x2y2 + 5x2y3 + -3x3y2 + -5x5 Combine like terms: 5x5 + -5x5 = 0 0 + -5y3 = -2x2y2 + 5x2y3 + -3x3y2 + -5x5 -5y3 = -2x2y2 + 5x2y3 + -3x3y2 + -5x5 Add '5y3' to each side of the equation. -5y3 + 5y3 = -2x2y2 + 5x2y3 + -3x3y2 + -5x5 + 5y3 Combine like terms: -5y3 + 5y3 = 0 0 = -2x2y2 + 5x2y3 + -3x3y2 + -5x5 + 5y3 Simplifying 0 = -2x2y2 + 5x2y3 + -3x3y2 + -5x5 + 5y3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

d = {0}

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