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

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


Simplifying
(y2) * dx + (x + -3) * dy = 0

Multiply y2 * dx
dxy2 + (x + -3) * dy = 0

Reorder the terms:
dxy2 + (-3 + x) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + dy(-3 + x) = 0
dxy2 + (-3 * dy + x * dy) = 0

Reorder the terms:
dxy2 + (dxy + -3dy) = 0
dxy2 + (dxy + -3dy) = 0

Reorder the terms:
dxy + dxy2 + -3dy = 0

Solving
dxy + dxy2 + -3dy = 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(x + xy + -3) = 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 '(x + xy + -3)' equal to zero and attempt to solve: Simplifying x + xy + -3 = 0 Reorder the terms: -3 + x + xy = 0 Solving -3 + x + xy = 0 Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + x + 3 + xy = 0 + 3 Reorder the terms: -3 + 3 + x + xy = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x + xy = 0 + 3 x + xy = 0 + 3 Combine like terms: 0 + 3 = 3 x + xy = 3 Add '-1x' to each side of the equation. x + -1x + xy = 3 + -1x Combine like terms: x + -1x = 0 0 + xy = 3 + -1x xy = 3 + -1x Add '-1xy' to each side of the equation. xy + -1xy = 3 + -1x + -1xy Combine like terms: xy + -1xy = 0 0 = 3 + -1x + -1xy Simplifying 0 = 3 + -1x + -1xy 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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