(2xy)dx+(4y+3x^2)dy=0

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Solution for (2xy)dx+(4y+3x^2)dy=0 equation:


Simplifying
(2xy) * dx + (4y + 3x2) * dy = 0

Remove parenthesis around (2xy)
2xy * dx + (4y + 3x2) * dy = 0

Multiply xy * dx
2dx2y + (4y + 3x2) * dy = 0

Reorder the terms:
2dx2y + (3x2 + 4y) * dy = 0

Reorder the terms for easier multiplication:
2dx2y + dy(3x2 + 4y) = 0
2dx2y + (3x2 * dy + 4y * dy) = 0
2dx2y + (3dx2y + 4dy2) = 0

Combine like terms: 2dx2y + 3dx2y = 5dx2y
5dx2y + 4dy2 = 0

Solving
5dx2y + 4dy2 = 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(5x2 + 4y) = 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 '(5x2 + 4y)' equal to zero and attempt to solve: Simplifying 5x2 + 4y = 0 Solving 5x2 + 4y = 0 Move all terms containing d to the left, all other terms to the right. Add '-5x2' to each side of the equation. 5x2 + -5x2 + 4y = 0 + -5x2 Combine like terms: 5x2 + -5x2 = 0 0 + 4y = 0 + -5x2 4y = 0 + -5x2 Remove the zero: 4y = -5x2 Add '-4y' to each side of the equation. 4y + -4y = -5x2 + -4y Combine like terms: 4y + -4y = 0 0 = -5x2 + -4y Simplifying 0 = -5x2 + -4y 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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