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

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


Simplifying
(3x2 + y) * dx + (x2y + -1x) * dy = 0

Reorder the terms for easier multiplication:
dx(3x2 + y) + (x2y + -1x) * dy = 0
(3x2 * dx + y * dx) + (x2y + -1x) * dy = 0

Reorder the terms:
(dxy + 3dx3) + (x2y + -1x) * dy = 0
(dxy + 3dx3) + (x2y + -1x) * dy = 0

Reorder the terms:
dxy + 3dx3 + (-1x + x2y) * dy = 0

Reorder the terms for easier multiplication:
dxy + 3dx3 + dy(-1x + x2y) = 0
dxy + 3dx3 + (-1x * dy + x2y * dy) = 0
dxy + 3dx3 + (-1dxy + dx2y2) = 0

Reorder the terms:
dxy + -1dxy + dx2y2 + 3dx3 = 0

Combine like terms: dxy + -1dxy = 0
0 + dx2y2 + 3dx3 = 0
dx2y2 + 3dx3 = 0

Solving
dx2y2 + 3dx3 = 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), 'dx2'.
dx2(y2 + 3x) = 0


Subproblem 1
Set the factor 'dx2' equal to zero and attempt to solve:

Simplifying
dx2 = 0

Solving
dx2 = 0

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

Simplifying
dx2 = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
y2 + 3x = 0

Reorder the terms:
3x + y2 = 0

Solving
3x + y2 = 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 + y2 = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + y2 = 0 + -3x
y2 = 0 + -3x
Remove the zero:
y2 = -3x

Add '-1y2' to each side of the equation.
y2 + -1y2 = -3x + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -3x + -1y2

Simplifying
0 = -3x + -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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