(x^2+3xy)dx+xdy=0

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Solution for (x^2+3xy)dx+xdy=0 equation: 


Simplifying
(x2 + 3xy) * dx + xdy = 0

Reorder the terms:
(3xy + x2) * dx + xdy = 0

Reorder the terms for easier multiplication:
dx(3xy + x2) + xdy = 0
(3xy * dx + x2 * dx) + xdy = 0
(3dx2y + dx3) + xdy = 0

Reorder the terms:
dxy + 3dx2y + dx3 = 0

Solving
dxy + 3dx2y + 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(y + 3xy + 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 '(y + 3xy + x2)' equal to zero and attempt to solve:

Simplifying
y + 3xy + x2 = 0

Reorder the terms:
3xy + x2 + y = 0

Solving
3xy + x2 + y = 0

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

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

Reorder the terms:
3xy + -3xy + x2 + y = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + x2 + y = 0 + -3xy
x2 + y = 0 + -3xy
Remove the zero:
x2 + y = -3xy

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

Combine like terms: x2 + -1x2 = 0
0 + y = -3xy + -1x2
y = -3xy + -1x2

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

Combine like terms: y + -1y = 0
0 = -3xy + -1x2 + -1y

Simplifying
0 = -3xy + -1x2 + -1y

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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