(2x^2-x)dx+(3xy^2+7x)dy=0

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Solution for (2x^2-x)dx+(3xy^2+7x)dy=0 equation:


Simplifying
(2x2 + -1x) * dx + (3xy2 + 7x) * dy = 0

Reorder the terms:
(-1x + 2x2) * dx + (3xy2 + 7x) * dy = 0

Reorder the terms for easier multiplication:
dx(-1x + 2x2) + (3xy2 + 7x) * dy = 0
(-1x * dx + 2x2 * dx) + (3xy2 + 7x) * dy = 0
(-1dx2 + 2dx3) + (3xy2 + 7x) * dy = 0

Reorder the terms:
-1dx2 + 2dx3 + (7x + 3xy2) * dy = 0

Reorder the terms for easier multiplication:
-1dx2 + 2dx3 + dy(7x + 3xy2) = 0
-1dx2 + 2dx3 + (7x * dy + 3xy2 * dy) = 0
-1dx2 + 2dx3 + (7dxy + 3dxy3) = 0

Reorder the terms:
7dxy + 3dxy3 + -1dx2 + 2dx3 = 0

Solving
7dxy + 3dxy3 + -1dx2 + 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), 'dx'.
dx(7y + 3y3 + -1x + 2x2) = 0

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(7y + 3y3 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying 7y + 3y3 + -1x + 2x2 = 0 Reorder the terms: -1x + 2x2 + 7y + 3y3 = 0 Solving -1x + 2x2 + 7y + 3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + 2x2 + 7y + x + 3y3 = 0 + x Reorder the terms: -1x + x + 2x2 + 7y + 3y3 = 0 + x Combine like terms: -1x + x = 0 0 + 2x2 + 7y + 3y3 = 0 + x 2x2 + 7y + 3y3 = 0 + x Remove the zero: 2x2 + 7y + 3y3 = x Add '-2x2' to each side of the equation. 2x2 + 7y + -2x2 + 3y3 = x + -2x2 Reorder the terms: 2x2 + -2x2 + 7y + 3y3 = x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 7y + 3y3 = x + -2x2 7y + 3y3 = x + -2x2 Add '-7y' to each side of the equation. 7y + -7y + 3y3 = x + -2x2 + -7y Combine like terms: 7y + -7y = 0 0 + 3y3 = x + -2x2 + -7y 3y3 = x + -2x2 + -7y Add '-3y3' to each side of the equation. 3y3 + -3y3 = x + -2x2 + -7y + -3y3 Combine like terms: 3y3 + -3y3 = 0 0 = x + -2x2 + -7y + -3y3 Simplifying 0 = x + -2x2 + -7y + -3y3 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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