(2x+y)dy-(4x+3y)dx=0

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Solution for (2x+y)dy-(4x+3y)dx=0 equation: 


Simplifying
(2x + y) * dy + -1(4x + 3y) * dx = 0

Reorder the terms for easier multiplication:
dy(2x + y) + -1(4x + 3y) * dx = 0
(2x * dy + y * dy) + -1(4x + 3y) * dx = 0
(2dxy + dy2) + -1(4x + 3y) * dx = 0

Reorder the terms for easier multiplication:
2dxy + dy2 + -1dx(4x + 3y) = 0
2dxy + dy2 + (4x * -1dx + 3y * -1dx) = 0

Reorder the terms:
2dxy + dy2 + (-3dxy + -4dx2) = 0
2dxy + dy2 + (-3dxy + -4dx2) = 0

Reorder the terms:
2dxy + -3dxy + -4dx2 + dy2 = 0

Combine like terms: 2dxy + -3dxy = -1dxy
-1dxy + -4dx2 + dy2 = 0

Solving
-1dxy + -4dx2 + 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(-1xy + -4x2 + 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 '(-1xy + -4x2 + y2)' equal to zero and attempt to solve:

Simplifying
-1xy + -4x2 + y2 = 0

Solving
-1xy + -4x2 + y2 = 0

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

Add 'xy' to each side of the equation.
-1xy + -4x2 + xy + y2 = 0 + xy

Reorder the terms:
-1xy + xy + -4x2 + y2 = 0 + xy

Combine like terms: -1xy + xy = 0
0 + -4x2 + y2 = 0 + xy
-4x2 + y2 = 0 + xy
Remove the zero:
-4x2 + y2 = xy

Add '4x2' to each side of the equation.
-4x2 + 4x2 + y2 = xy + 4x2

Combine like terms: -4x2 + 4x2 = 0
0 + y2 = xy + 4x2
y2 = xy + 4x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = xy + 4x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = xy + 4x2 + -1y2

Simplifying
0 = xy + 4x2 + -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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