x(1+y)dx+(x^2y^2+x^2+y^2+1)dy=0

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Solution for x(1+y)dx+(x^2y^2+x^2+y^2+1)dy=0 equation:


Simplifying
x(1 + y) * dx + (x2y2 + x2 + y2 + 1) * dy = 0

Reorder the terms for easier multiplication:
x * dx(1 + y) + (x2y2 + x2 + y2 + 1) * dy = 0

Multiply x * dx
dx2(1 + y) + (x2y2 + x2 + y2 + 1) * dy = 0
(1 * dx2 + y * dx2) + (x2y2 + x2 + y2 + 1) * dy = 0
(1dx2 + dx2y) + (x2y2 + x2 + y2 + 1) * dy = 0

Reorder the terms:
1dx2 + dx2y + (1 + x2 + x2y2 + y2) * dy = 0

Reorder the terms for easier multiplication:
1dx2 + dx2y + dy(1 + x2 + x2y2 + y2) = 0
1dx2 + dx2y + (1 * dy + x2 * dy + x2y2 * dy + y2 * dy) = 0

Reorder the terms:
1dx2 + dx2y + (dx2y + dx2y3 + 1dy + dy3) = 0
1dx2 + dx2y + (dx2y + dx2y3 + 1dy + dy3) = 0

Combine like terms: dx2y + dx2y = 2dx2y
1dx2 + 2dx2y + dx2y3 + 1dy + dy3 = 0

Solving
1dx2 + 2dx2y + dx2y3 + 1dy + dy3 = 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(x2 + 2x2y + x2y3 + y + y3) = 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 '(x2 + 2x2y + x2y3 + y + y3)' equal to zero and attempt to solve: Simplifying x2 + 2x2y + x2y3 + y + y3 = 0 Solving x2 + 2x2y + x2y3 + y + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + 2x2y + x2y3 + y + -1x2 + y3 = 0 + -1x2 Reorder the terms: x2 + -1x2 + 2x2y + x2y3 + y + y3 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2x2y + x2y3 + y + y3 = 0 + -1x2 2x2y + x2y3 + y + y3 = 0 + -1x2 Remove the zero: 2x2y + x2y3 + y + y3 = -1x2 Add '-2x2y' to each side of the equation. 2x2y + x2y3 + y + -2x2y + y3 = -1x2 + -2x2y Reorder the terms: 2x2y + -2x2y + x2y3 + y + y3 = -1x2 + -2x2y Combine like terms: 2x2y + -2x2y = 0 0 + x2y3 + y + y3 = -1x2 + -2x2y x2y3 + y + y3 = -1x2 + -2x2y Add '-1x2y3' to each side of the equation. x2y3 + y + -1x2y3 + y3 = -1x2 + -2x2y + -1x2y3 Reorder the terms: x2y3 + -1x2y3 + y + y3 = -1x2 + -2x2y + -1x2y3 Combine like terms: x2y3 + -1x2y3 = 0 0 + y + y3 = -1x2 + -2x2y + -1x2y3 y + y3 = -1x2 + -2x2y + -1x2y3 Add '-1y' to each side of the equation. y + -1y + y3 = -1x2 + -2x2y + -1x2y3 + -1y Combine like terms: y + -1y = 0 0 + y3 = -1x2 + -2x2y + -1x2y3 + -1y y3 = -1x2 + -2x2y + -1x2y3 + -1y Add '-1y3' to each side of the equation. y3 + -1y3 = -1x2 + -2x2y + -1x2y3 + -1y + -1y3 Combine like terms: y3 + -1y3 = 0 0 = -1x2 + -2x2y + -1x2y3 + -1y + -1y3 Simplifying 0 = -1x2 + -2x2y + -1x2y3 + -1y + -1y3 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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