solve(3y-7x+7)dx+(7y-3x+3)dy=0

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Solution for solve(3y-7x+7)dx+(7y-3x+3)dy=0 equation:


Simplifying
solve(3y + -7x + 7) * dx + (7y + -3x + 3) * dy = 0

Reorder the terms:
elosv(7 + -7x + 3y) * dx + (7y + -3x + 3) * dy = 0

Reorder the terms for easier multiplication:
elosv * dx(7 + -7x + 3y) + (7y + -3x + 3) * dy = 0

Multiply elosv * dx
delosvx(7 + -7x + 3y) + (7y + -3x + 3) * dy = 0
(7 * delosvx + -7x * delosvx + 3y * delosvx) + (7y + -3x + 3) * dy = 0

Reorder the terms:
(7delosvx + 3delosvxy + -7delosvx2) + (7y + -3x + 3) * dy = 0
(7delosvx + 3delosvxy + -7delosvx2) + (7y + -3x + 3) * dy = 0

Reorder the terms:
7delosvx + 3delosvxy + -7delosvx2 + (3 + -3x + 7y) * dy = 0

Reorder the terms for easier multiplication:
7delosvx + 3delosvxy + -7delosvx2 + dy(3 + -3x + 7y) = 0
7delosvx + 3delosvxy + -7delosvx2 + (3 * dy + -3x * dy + 7y * dy) = 0

Reorder the terms:
7delosvx + 3delosvxy + -7delosvx2 + (-3dxy + 3dy + 7dy2) = 0
7delosvx + 3delosvxy + -7delosvx2 + (-3dxy + 3dy + 7dy2) = 0

Solving
7delosvx + 3delosvxy + -7delosvx2 + -3dxy + 3dy + 7dy2 = 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(7elosvx + 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2) = 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 '(7elosvx + 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2)' equal to zero and attempt to solve: Simplifying 7elosvx + 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = 0 Solving 7elosvx + 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-7elosvx' to each side of the equation. 7elosvx + 3elosvxy + -7elosvx2 + -3xy + 3y + -7elosvx + 7y2 = 0 + -7elosvx Reorder the terms: 7elosvx + -7elosvx + 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = 0 + -7elosvx Combine like terms: 7elosvx + -7elosvx = 0 0 + 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = 0 + -7elosvx 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = 0 + -7elosvx Remove the zero: 3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = -7elosvx Add '-3elosvxy' to each side of the equation. 3elosvxy + -7elosvx2 + -3xy + 3y + -3elosvxy + 7y2 = -7elosvx + -3elosvxy Reorder the terms: 3elosvxy + -3elosvxy + -7elosvx2 + -3xy + 3y + 7y2 = -7elosvx + -3elosvxy Combine like terms: 3elosvxy + -3elosvxy = 0 0 + -7elosvx2 + -3xy + 3y + 7y2 = -7elosvx + -3elosvxy -7elosvx2 + -3xy + 3y + 7y2 = -7elosvx + -3elosvxy Add '7elosvx2' to each side of the equation. -7elosvx2 + -3xy + 3y + 7elosvx2 + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 Reorder the terms: -7elosvx2 + 7elosvx2 + -3xy + 3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 Combine like terms: -7elosvx2 + 7elosvx2 = 0 0 + -3xy + 3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 -3xy + 3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 Add '3xy' to each side of the equation. -3xy + 3y + 3xy + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy Reorder the terms: -3xy + 3xy + 3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy Combine like terms: -3xy + 3xy = 0 0 + 3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy 3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy Add '-3y' to each side of the equation. 3y + -3y + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy + -3y Combine like terms: 3y + -3y = 0 0 + 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy + -3y 7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy + -3y Add '-7y2' to each side of the equation. 7y2 + -7y2 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy + -3y + -7y2 Combine like terms: 7y2 + -7y2 = 0 0 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy + -3y + -7y2 Simplifying 0 = -7elosvx + -3elosvxy + 7elosvx2 + 3xy + -3y + -7y2 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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