(1+x^3)dy-(x^2y)dy=0

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Solution for (1+x^3)dy-(x^2y)dy=0 equation:


Simplifying
(1 + x3) * dy + -1(x2y) * dy = 0

Reorder the terms for easier multiplication:
dy(1 + x3) + -1(x2y) * dy = 0
(1 * dy + x3 * dy) + -1(x2y) * dy = 0

Reorder the terms:
(dx3y + 1dy) + -1(x2y) * dy = 0
(dx3y + 1dy) + -1(x2y) * dy = 0

Multiply x2y * dy
dx3y + 1dy + -1dx2y2 = 0

Reorder the terms:
-1dx2y2 + dx3y + 1dy = 0

Solving
-1dx2y2 + dx3y + 1dy = 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), 'dy'.
dy(-1x2y + x3 + 1) = 0

Subproblem 1

Set the factor 'dy' equal to zero and attempt to solve: Simplifying dy = 0 Solving dy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dy = 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 '(-1x2y + x3 + 1)' equal to zero and attempt to solve: Simplifying -1x2y + x3 + 1 = 0 Reorder the terms: 1 + -1x2y + x3 = 0 Solving 1 + -1x2y + x3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1x2y + -1 + x3 = 0 + -1 Reorder the terms: 1 + -1 + -1x2y + x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x2y + x3 = 0 + -1 -1x2y + x3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x2y + x3 = -1 Add 'x2y' to each side of the equation. -1x2y + x2y + x3 = -1 + x2y Combine like terms: -1x2y + x2y = 0 0 + x3 = -1 + x2y x3 = -1 + x2y Add '-1x3' to each side of the equation. x3 + -1x3 = -1 + x2y + -1x3 Combine like terms: x3 + -1x3 = 0 0 = -1 + x2y + -1x3 Simplifying 0 = -1 + x2y + -1x3 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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