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

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


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

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

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

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

Reorder the terms for easier multiplication:
dxy + 2dx3 + fy(-1x + x2y) = 0
dxy + 2dx3 + (-1x * fy + x2y * fy) = 0
dxy + 2dx3 + (-1fxy + fx2y2) = 0

Solving
dxy + 2dx3 + -1fxy + fx2y2 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add 'fxy' to each side of the equation.
dxy + 2dx3 + -1fxy + fxy + fx2y2 = 0 + fxy

Combine like terms: -1fxy + fxy = 0
dxy + 2dx3 + 0 + fx2y2 = 0 + fxy
dxy + 2dx3 + fx2y2 = 0 + fxy
Remove the zero:
dxy + 2dx3 + fx2y2 = fxy

Add '-1fx2y2' to each side of the equation.
dxy + 2dx3 + fx2y2 + -1fx2y2 = fxy + -1fx2y2

Combine like terms: fx2y2 + -1fx2y2 = 0
dxy + 2dx3 + 0 = fxy + -1fx2y2
dxy + 2dx3 = fxy + -1fx2y2

Reorder the terms:
dxy + 2dx3 + -1fxy + fx2y2 = fxy + -1fxy + -1fx2y2 + fx2y2

Combine like terms: fxy + -1fxy = 0
dxy + 2dx3 + -1fxy + fx2y2 = 0 + -1fx2y2 + fx2y2
dxy + 2dx3 + -1fxy + fx2y2 = -1fx2y2 + fx2y2

Combine like terms: -1fx2y2 + fx2y2 = 0
dxy + 2dx3 + -1fxy + fx2y2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(dy + 2dx2 + -1fy + fxy2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(dy + 2dx2 + -1fy + fxy2)' equal to zero and attempt to solve: Simplifying dy + 2dx2 + -1fy + fxy2 = 0 Reorder the terms: 2dx2 + dy + fxy2 + -1fy = 0 Solving 2dx2 + dy + fxy2 + -1fy = 0 Move all terms containing d to the left, all other terms to the right. Add '-1fxy2' to each side of the equation. 2dx2 + dy + fxy2 + -1fxy2 + -1fy = 0 + -1fxy2 Combine like terms: fxy2 + -1fxy2 = 0 2dx2 + dy + 0 + -1fy = 0 + -1fxy2 2dx2 + dy + -1fy = 0 + -1fxy2 Remove the zero: 2dx2 + dy + -1fy = -1fxy2 Add 'fy' to each side of the equation. 2dx2 + dy + -1fy + fy = -1fxy2 + fy Combine like terms: -1fy + fy = 0 2dx2 + dy + 0 = -1fxy2 + fy 2dx2 + dy = -1fxy2 + fy 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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