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

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Solution for (1+x^2)dy-2x(y+3)dx=0 equation: 


Simplifying
(1 + x2) * dy + -2x(y + 3) * dx = 0

Reorder the terms for easier multiplication:
dy(1 + x2) + -2x(y + 3) * dx = 0
(1 * dy + x2 * dy) + -2x(y + 3) * dx = 0

Reorder the terms:
(dx2y + 1dy) + -2x(y + 3) * dx = 0
(dx2y + 1dy) + -2x(y + 3) * dx = 0

Reorder the terms:
dx2y + 1dy + -2x(3 + y) * dx = 0

Reorder the terms for easier multiplication:
dx2y + 1dy + -2x * dx(3 + y) = 0

Multiply x * dx
dx2y + 1dy + -2dx2(3 + y) = 0
dx2y + 1dy + (3 * -2dx2 + y * -2dx2) = 0
dx2y + 1dy + (-6dx2 + -2dx2y) = 0

Reorder the terms:
-6dx2 + dx2y + -2dx2y + 1dy = 0

Combine like terms: dx2y + -2dx2y = -1dx2y
-6dx2 + -1dx2y + 1dy = 0

Solving
-6dx2 + -1dx2y + 1dy = 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(-6x2 + -1x2y + 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 '(-6x2 + -1x2y + y)' equal to zero and attempt to solve:

Simplifying
-6x2 + -1x2y + y = 0

Solving
-6x2 + -1x2y + y = 0

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

Add '6x2' to each side of the equation.
-6x2 + -1x2y + 6x2 + y = 0 + 6x2

Reorder the terms:
-6x2 + 6x2 + -1x2y + y = 0 + 6x2

Combine like terms: -6x2 + 6x2 = 0
0 + -1x2y + y = 0 + 6x2
-1x2y + y = 0 + 6x2
Remove the zero:
-1x2y + y = 6x2

Add 'x2y' to each side of the equation.
-1x2y + x2y + y = 6x2 + x2y

Combine like terms: -1x2y + x2y = 0
0 + y = 6x2 + x2y
y = 6x2 + x2y

Add '-1y' to each side of the equation.
y + -1y = 6x2 + x2y + -1y

Combine like terms: y + -1y = 0
0 = 6x2 + x2y + -1y

Simplifying
0 = 6x2 + x2y + -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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