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

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


Simplifying
(2x2 + y) * dx + (x2y + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(2x2 + y) + (x2y + -1x) * dy = 0
(2x2 * dx + y * dx) + (x2y + -1x) * dy = 0

Reorder the terms:
(dxy + 2dx3) + (x2y + -1x) * dy = 0
(dxy + 2dx3) + (x2y + -1x) * dy = 0

Reorder the terms:
dxy + 2dx3 + (-1x + x2y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 2dx3 + dy(-1x + x2y) = 0
dxy + 2dx3 + (-1x * dy + x2y * dy) = 0
dxy + 2dx3 + (-1dxy + dx2y2) = 0

Reorder the terms:
dxy + -1dxy + dx2y2 + 2dx3 = 0

Combine like terms: dxy + -1dxy = 0
0 + dx2y2 + 2dx3 = 0
dx2y2 + 2dx3 = 0

Solving
dx2y2 + 2dx3 = 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), 'dx2'.
dx2(y2 + 2x) = 0

Subproblem 1

Set the factor 'dx2' equal to zero and attempt to solve: Simplifying dx2 = 0 Solving dx2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2 = 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 '(y2 + 2x)' equal to zero and attempt to solve: Simplifying y2 + 2x = 0 Reorder the terms: 2x + y2 = 0 Solving 2x + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + y2 = 0 + -2x Combine like terms: 2x + -2x = 0 0 + y2 = 0 + -2x y2 = 0 + -2x Remove the zero: y2 = -2x Add '-1y2' to each side of the equation. y2 + -1y2 = -2x + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -2x + -1y2 Simplifying 0 = -2x + -1y2 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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