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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