(3x-5)dx+(x+y)dy=0

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Solution for (3x-5)dx+(x+y)dy=0 equation: 


Simplifying
(3x + -5) * dx + (x + y) * dy = 0

Reorder the terms:
(-5 + 3x) * dx + (x + y) * dy = 0

Reorder the terms for easier multiplication:
dx(-5 + 3x) + (x + y) * dy = 0
(-5 * dx + 3x * dx) + (x + y) * dy = 0
(-5dx + 3dx2) + (x + y) * dy = 0

Reorder the terms for easier multiplication:
-5dx + 3dx2 + dy(x + y) = 0
-5dx + 3dx2 + (x * dy + y * dy) = 0
-5dx + 3dx2 + (dxy + dy2) = 0

Reorder the terms:
-5dx + dxy + 3dx2 + dy2 = 0

Solving
-5dx + dxy + 3dx2 + 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(-5x + xy + 3x2 + 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 '(-5x + xy + 3x2 + y2)' equal to zero and attempt to solve:

Simplifying
-5x + xy + 3x2 + y2 = 0

Solving
-5x + xy + 3x2 + y2 = 0

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

Add '5x' to each side of the equation.
-5x + xy + 3x2 + 5x + y2 = 0 + 5x

Reorder the terms:
-5x + 5x + xy + 3x2 + y2 = 0 + 5x

Combine like terms: -5x + 5x = 0
0 + xy + 3x2 + y2 = 0 + 5x
xy + 3x2 + y2 = 0 + 5x
Remove the zero:
xy + 3x2 + y2 = 5x

Add '-1xy' to each side of the equation.
xy + 3x2 + -1xy + y2 = 5x + -1xy

Reorder the terms:
xy + -1xy + 3x2 + y2 = 5x + -1xy

Combine like terms: xy + -1xy = 0
0 + 3x2 + y2 = 5x + -1xy
3x2 + y2 = 5x + -1xy

Add '-3x2' to each side of the equation.
3x2 + -3x2 + y2 = 5x + -1xy + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + y2 = 5x + -1xy + -3x2
y2 = 5x + -1xy + -3x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = 5x + -1xy + -3x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = 5x + -1xy + -3x2 + -1y2

Simplifying
0 = 5x + -1xy + -3x2 + -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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