solve(x+2y)dx+(2x+y)dy=0

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Solution for solve(x+2y)dx+(2x+y)dy=0 equation:


Simplifying
solve(x + 2y) * dx + (2x + y) * dy = 0

Reorder the terms for easier multiplication:
elosv * dx(x + 2y) + (2x + y) * dy = 0

Multiply elosv * dx
delosvx(x + 2y) + (2x + y) * dy = 0
(x * delosvx + 2y * delosvx) + (2x + y) * dy = 0

Reorder the terms:
(2delosvxy + delosvx2) + (2x + y) * dy = 0
(2delosvxy + delosvx2) + (2x + y) * dy = 0

Reorder the terms for easier multiplication:
2delosvxy + delosvx2 + dy(2x + y) = 0
2delosvxy + delosvx2 + (2x * dy + y * dy) = 0
2delosvxy + delosvx2 + (2dxy + dy2) = 0

Solving
2delosvxy + delosvx2 + 2dxy + dy2 = 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(2elosvxy + elosvx2 + 2xy + y2) = 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 '(2elosvxy + elosvx2 + 2xy + y2)' equal to zero and attempt to solve: Simplifying 2elosvxy + elosvx2 + 2xy + y2 = 0 Solving 2elosvxy + elosvx2 + 2xy + y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-2elosvxy' to each side of the equation. 2elosvxy + elosvx2 + 2xy + -2elosvxy + y2 = 0 + -2elosvxy Reorder the terms: 2elosvxy + -2elosvxy + elosvx2 + 2xy + y2 = 0 + -2elosvxy Combine like terms: 2elosvxy + -2elosvxy = 0 0 + elosvx2 + 2xy + y2 = 0 + -2elosvxy elosvx2 + 2xy + y2 = 0 + -2elosvxy Remove the zero: elosvx2 + 2xy + y2 = -2elosvxy Add '-1elosvx2' to each side of the equation. elosvx2 + 2xy + -1elosvx2 + y2 = -2elosvxy + -1elosvx2 Reorder the terms: elosvx2 + -1elosvx2 + 2xy + y2 = -2elosvxy + -1elosvx2 Combine like terms: elosvx2 + -1elosvx2 = 0 0 + 2xy + y2 = -2elosvxy + -1elosvx2 2xy + y2 = -2elosvxy + -1elosvx2 Add '-2xy' to each side of the equation. 2xy + -2xy + y2 = -2elosvxy + -1elosvx2 + -2xy Combine like terms: 2xy + -2xy = 0 0 + y2 = -2elosvxy + -1elosvx2 + -2xy y2 = -2elosvxy + -1elosvx2 + -2xy Add '-1y2' to each side of the equation. y2 + -1y2 = -2elosvxy + -1elosvx2 + -2xy + -1y2 Combine like terms: y2 + -1y2 = 0 0 = -2elosvxy + -1elosvx2 + -2xy + -1y2 Simplifying 0 = -2elosvxy + -1elosvx2 + -2xy + -1y2 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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