xdy+(x+y)DX=0

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Solution for xdy+(x+y)DX=0 equation: 


Simplifying
xdy + (x + y) * DX = 0

Reorder the terms for easier multiplication:
dxy + DX(x + y) = 0
dxy + (x * DX + y * DX) = 0
dxy + (xDX + yDX) = 0

Solving
dxy + xDX + yDX = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-1xDX' to each side of the equation.
dxy + xDX + -1xDX + yDX = 0 + -1xDX

Combine like terms: xDX + -1xDX = 0
dxy + 0 + yDX = 0 + -1xDX
dxy + yDX = 0 + -1xDX
Remove the zero:
dxy + yDX = -1xDX

Add '-1yDX' to each side of the equation.
dxy + yDX + -1yDX = -1xDX + -1yDX

Combine like terms: yDX + -1yDX = 0
dxy + 0 = -1xDX + -1yDX
dxy = -1xDX + -1yDX

Divide each side by 'xy'.
d = -1y-1DX + -1x-1DX

Simplifying
d = -1y-1DX + -1x-1DX

Reorder the terms:
d = -1x-1DX + -1y-1DX

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