xy*dy+(4x+x^2)*dx=0

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Solution for xy*dy+(4x+x^2)*dx=0 equation: 


Simplifying
xy * dy + (4x + x2) * dx = 0

Multiply xy * dy
dxy2 + (4x + x2) * dx = 0

Reorder the terms for easier multiplication:
dxy2 + dx(4x + x2) = 0
dxy2 + (4x * dx + x2 * dx) = 0
dxy2 + (4dx2 + dx3) = 0

Solving
dxy2 + 4dx2 + dx3 = 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), 'dx'.
dx(y2 + 4x + x2) = 0


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

Simplifying
dx = 0

Solving
dx = 0

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

Simplifying
dx = 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 '(y2 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
y2 + 4x + x2 = 0

Reorder the terms:
4x + x2 + y2 = 0

Solving
4x + x2 + y2 = 0

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

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

Reorder the terms:
4x + -4x + x2 + y2 = 0 + -4x

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

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

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

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

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

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

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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