(x+4y)dy+2ydx=0

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Solution for (x+4y)dy+2ydx=0 equation: 


Simplifying
(x + 4y) * dy + 2ydx = 0

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

Reorder the terms:
dxy + 2dxy + 4dy2 = 0

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

Solving
3dxy + 4dy2 = 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), 'dy'.
dy(3x + 4y) = 0


Subproblem 1
Set the factor 'dy' equal to zero and attempt to solve:

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-3x' to each side of the equation.
3x + -3x + 4y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 4y = 0 + -3x
4y = 0 + -3x
Remove the zero:
4y = -3x

Add '-4y' to each side of the equation.
4y + -4y = -3x + -4y

Combine like terms: 4y + -4y = 0
0 = -3x + -4y

Simplifying
0 = -3x + -4y

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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