(ex+y)dy-(x+3y)dx=0

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


Simplifying
(ex + y) * dy + -1(x + 3y) * dx = 0

Reorder the terms for easier multiplication:
dy(ex + y) + -1(x + 3y) * dx = 0
(ex * dy + y * dy) + -1(x + 3y) * dx = 0
(dexy + dy2) + -1(x + 3y) * dx = 0

Reorder the terms for easier multiplication:
dexy + dy2 + -1dx(x + 3y) = 0
dexy + dy2 + (x * -1dx + 3y * -1dx) = 0

Reorder the terms:
dexy + dy2 + (-3dxy + -1dx2) = 0
dexy + dy2 + (-3dxy + -1dx2) = 0

Reorder the terms:
dexy + -3dxy + -1dx2 + dy2 = 0

Solving
dexy + -3dxy + -1dx2 + 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(exy + -3xy + -1x2 + 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 '(exy + -3xy + -1x2 + y2)' equal to zero and attempt to solve:

Simplifying
exy + -3xy + -1x2 + y2 = 0

Solving
exy + -3xy + -1x2 + y2 = 0

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

Add '-1exy' to each side of the equation.
exy + -3xy + -1x2 + -1exy + y2 = 0 + -1exy

Reorder the terms:
exy + -1exy + -3xy + -1x2 + y2 = 0 + -1exy

Combine like terms: exy + -1exy = 0
0 + -3xy + -1x2 + y2 = 0 + -1exy
-3xy + -1x2 + y2 = 0 + -1exy
Remove the zero:
-3xy + -1x2 + y2 = -1exy

Add '3xy' to each side of the equation.
-3xy + -1x2 + 3xy + y2 = -1exy + 3xy

Reorder the terms:
-3xy + 3xy + -1x2 + y2 = -1exy + 3xy

Combine like terms: -3xy + 3xy = 0
0 + -1x2 + y2 = -1exy + 3xy
-1x2 + y2 = -1exy + 3xy

Add 'x2' to each side of the equation.
-1x2 + x2 + y2 = -1exy + 3xy + x2

Combine like terms: -1x2 + x2 = 0
0 + y2 = -1exy + 3xy + x2
y2 = -1exy + 3xy + x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -1exy + 3xy + x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -1exy + 3xy + x2 + -1y2

Simplifying
0 = -1exy + 3xy + x2 + -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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