(y)dy-(4x)dx=0

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


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

Multiply y * dy
dy2 + -1(4x) * dx = 0

Remove parenthesis around (4x)
dy2 + -1 * 4x * dx = 0

Multiply -1 * 4
dy2 + -4x * dx = 0

Multiply x * dx
dy2 + -4dx2 = 0

Reorder the terms:
-4dx2 + dy2 = 0

Solving
-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(-4x2 + y2) = 0

Factor a difference between two squares.
d((2x + y)(-2x + y)) = 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 '(2x + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-2x' to each side of the equation.
2x + -2x + y = 0 + -2x

Combine like terms: 2x + -2x = 0
0 + y = 0 + -2x
y = 0 + -2x
Remove the zero:
y = -2x

Add '-1y' to each side of the equation.
y + -1y = -2x + -1y

Combine like terms: y + -1y = 0
0 = -2x + -1y

Simplifying
0 = -2x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(-2x + y)' equal to zero and attempt to solve:

Simplifying
-2x + y = 0

Solving
-2x + y = 0

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

Add '2x' to each side of the equation.
-2x + 2x + y = 0 + 2x

Combine like terms: -2x + 2x = 0
0 + y = 0 + 2x
y = 0 + 2x
Remove the zero:
y = 2x

Add '-1y' to each side of the equation.
y + -1y = 2x + -1y

Combine like terms: y + -1y = 0
0 = 2x + -1y

Simplifying
0 = 2x + -1y

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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