Y(axy+ex)dx-exdy=0

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Solution for Y(axy+ex)dx-exdy=0 equation: 


Simplifying
Y(axy + ex) * dx + -1exdy = 0

Reorder the terms for easier multiplication:
Y * dx(axy + ex) + -1exdy = 0

Multiply Y * dx
dxY(axy + ex) + -1exdy = 0
(axy * dxY + ex * dxY) + -1exdy = 0
(adx2yY + dex2Y) + -1exdy = 0

Reorder the terms:
adx2yY + -1dexy + dex2Y = 0

Solving
adx2yY + -1dexy + dex2Y = 0

Solving for variable 'a'.

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

Add 'dexy' to each side of the equation.
adx2yY + -1dexy + dexy + dex2Y = 0 + dexy

Combine like terms: -1dexy + dexy = 0
adx2yY + 0 + dex2Y = 0 + dexy
adx2yY + dex2Y = 0 + dexy
Remove the zero:
adx2yY + dex2Y = dexy

Add '-1dex2Y' to each side of the equation.
adx2yY + dex2Y + -1dex2Y = dexy + -1dex2Y

Combine like terms: dex2Y + -1dex2Y = 0
adx2yY + 0 = dexy + -1dex2Y
adx2yY = dexy + -1dex2Y

Divide each side by 'dx2yY'.
a = ex-1Y-1 + -1ey-1

Simplifying
a = ex-1Y-1 + -1ey-1

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