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

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


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

Remove parenthesis around (2xy)
2xy * dx + (x2 + -1y) * dy = 0

Multiply xy * dx
2dx2y + (x2 + -1y) * dy = 0

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

Combine like terms: 2dx2y + dx2y = 3dx2y
3dx2y + -1dy2 = 0

Solving
3dx2y + -1dy2 = 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(3x2 + -1y) = 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 '(3x2 + -1y)' equal to zero and attempt to solve: Simplifying 3x2 + -1y = 0 Solving 3x2 + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x2' to each side of the equation. 3x2 + -3x2 + -1y = 0 + -3x2 Combine like terms: 3x2 + -3x2 = 0 0 + -1y = 0 + -3x2 -1y = 0 + -3x2 Remove the zero: -1y = -3x2 Add 'y' to each side of the equation. -1y + y = -3x2 + y Combine like terms: -1y + y = 0 0 = -3x2 + y Simplifying 0 = -3x2 + y 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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