(y^2+2xy)dx+(2X^2+3xy)dy=0

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Solution for (y^2+2xy)dx+(2X^2+3xy)dy=0 equation:


Simplifying
(y2 + 2xy) * dx + (2X2 + 3xy) * dy = 0

Reorder the terms:
(2xy + y2) * dx + (2X2 + 3xy) * dy = 0

Reorder the terms for easier multiplication:
dx(2xy + y2) + (2X2 + 3xy) * dy = 0
(2xy * dx + y2 * dx) + (2X2 + 3xy) * dy = 0

Reorder the terms:
(dxy2 + 2dx2y) + (2X2 + 3xy) * dy = 0
(dxy2 + 2dx2y) + (2X2 + 3xy) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 2dx2y + dy(2X2 + 3xy) = 0
dxy2 + 2dx2y + (2X2 * dy + 3xy * dy) = 0

Reorder the terms:
dxy2 + 2dx2y + (3dxy2 + 2dyX2) = 0
dxy2 + 2dx2y + (3dxy2 + 2dyX2) = 0

Reorder the terms:
dxy2 + 3dxy2 + 2dx2y + 2dyX2 = 0

Combine like terms: dxy2 + 3dxy2 = 4dxy2
4dxy2 + 2dx2y + 2dyX2 = 0

Solving
4dxy2 + 2dx2y + 2dyX2 = 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), '2dy'.
2dy(2xy + x2 + X2) = 0

Ignore the factor 2.

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 '(2xy + x2 + X2)' equal to zero and attempt to solve: Simplifying 2xy + x2 + X2 = 0 Reorder the terms: X2 + 2xy + x2 = 0 Solving X2 + 2xy + x2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1X2' to each side of the equation. X2 + 2xy + -1X2 + x2 = 0 + -1X2 Reorder the terms: X2 + -1X2 + 2xy + x2 = 0 + -1X2 Combine like terms: X2 + -1X2 = 0 0 + 2xy + x2 = 0 + -1X2 2xy + x2 = 0 + -1X2 Remove the zero: 2xy + x2 = -1X2 Add '-2xy' to each side of the equation. 2xy + -2xy + x2 = -1X2 + -2xy Combine like terms: 2xy + -2xy = 0 0 + x2 = -1X2 + -2xy x2 = -1X2 + -2xy Add '-1x2' to each side of the equation. x2 + -1x2 = -1X2 + -2xy + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -1X2 + -2xy + -1x2 Simplifying 0 = -1X2 + -2xy + -1x2 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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