(2xy+3)dx+(x^2+8y)dy=0

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Solution for (2xy+3)dx+(x^2+8y)dy=0 equation:


Simplifying
(2xy + 3) * dx + (x2 + 8y) * dy = 0

Reorder the terms:
(3 + 2xy) * dx + (x2 + 8y) * dy = 0

Reorder the terms for easier multiplication:
dx(3 + 2xy) + (x2 + 8y) * dy = 0
(3 * dx + 2xy * dx) + (x2 + 8y) * dy = 0
(3dx + 2dx2y) + (x2 + 8y) * dy = 0

Reorder the terms for easier multiplication:
3dx + 2dx2y + dy(x2 + 8y) = 0
3dx + 2dx2y + (x2 * dy + 8y * dy) = 0
3dx + 2dx2y + (dx2y + 8dy2) = 0

Combine like terms: 2dx2y + dx2y = 3dx2y
3dx + 3dx2y + 8dy2 = 0

Solving
3dx + 3dx2y + 8dy2 = 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), 'd'.
d(3x + 3x2y + 8y2) = 0

Subproblem 1

Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0

Subproblem 2

Set the factor '(3x + 3x2y + 8y2)' equal to zero and attempt to solve: Simplifying 3x + 3x2y + 8y2 = 0 Solving 3x + 3x2y + 8y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-3x' to each side of the equation. 3x + 3x2y + -3x + 8y2 = 0 + -3x Reorder the terms: 3x + -3x + 3x2y + 8y2 = 0 + -3x Combine like terms: 3x + -3x = 0 0 + 3x2y + 8y2 = 0 + -3x 3x2y + 8y2 = 0 + -3x Remove the zero: 3x2y + 8y2 = -3x Add '-3x2y' to each side of the equation. 3x2y + -3x2y + 8y2 = -3x + -3x2y Combine like terms: 3x2y + -3x2y = 0 0 + 8y2 = -3x + -3x2y 8y2 = -3x + -3x2y Add '-8y2' to each side of the equation. 8y2 + -8y2 = -3x + -3x2y + -8y2 Combine like terms: 8y2 + -8y2 = 0 0 = -3x + -3x2y + -8y2 Simplifying 0 = -3x + -3x2y + -8y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

d = {0}

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