y(4x+y)dx-2(x^2-y)dy=0

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Solution for y(4x+y)dx-2(x^2-y)dy=0 equation:


Simplifying
y(4x + y) * dx + -2(x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
y * dx(4x + y) + -2(x2 + -1y) * dy = 0

Multiply y * dx
dxy(4x + y) + -2(x2 + -1y) * dy = 0
(4x * dxy + y * dxy) + -2(x2 + -1y) * dy = 0

Reorder the terms:
(dxy2 + 4dx2y) + -2(x2 + -1y) * dy = 0
(dxy2 + 4dx2y) + -2(x2 + -1y) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + 4dx2y + -2dy(x2 + -1y) = 0
dxy2 + 4dx2y + (x2 * -2dy + -1y * -2dy) = 0
dxy2 + 4dx2y + (-2dx2y + 2dy2) = 0

Combine like terms: 4dx2y + -2dx2y = 2dx2y
dxy2 + 2dx2y + 2dy2 = 0

Solving
dxy2 + 2dx2y + 2dy2 = 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(xy + 2x2 + 2y) = 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 '(xy + 2x2 + 2y)' equal to zero and attempt to solve: Simplifying xy + 2x2 + 2y = 0 Solving xy + 2x2 + 2y = 0 Move all terms containing d to the left, all other terms to the right. Add '-1xy' to each side of the equation. xy + 2x2 + -1xy + 2y = 0 + -1xy Reorder the terms: xy + -1xy + 2x2 + 2y = 0 + -1xy Combine like terms: xy + -1xy = 0 0 + 2x2 + 2y = 0 + -1xy 2x2 + 2y = 0 + -1xy Remove the zero: 2x2 + 2y = -1xy Add '-2x2' to each side of the equation. 2x2 + -2x2 + 2y = -1xy + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 + 2y = -1xy + -2x2 2y = -1xy + -2x2 Add '-2y' to each side of the equation. 2y + -2y = -1xy + -2x2 + -2y Combine like terms: 2y + -2y = 0 0 = -1xy + -2x2 + -2y Simplifying 0 = -1xy + -2x2 + -2y 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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