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

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Solution for (5-x^2)dy+(3+3Y)dx=0 equation: 


Simplifying
(5 + -1x2) * dy + (3 + 3Y) * dx = 0

Reorder the terms for easier multiplication:
dy(5 + -1x2) + (3 + 3Y) * dx = 0
(5 * dy + -1x2 * dy) + (3 + 3Y) * dx = 0

Reorder the terms:
(-1dx2y + 5dy) + (3 + 3Y) * dx = 0
(-1dx2y + 5dy) + (3 + 3Y) * dx = 0

Reorder the terms for easier multiplication:
-1dx2y + 5dy + dx(3 + 3Y) = 0
-1dx2y + 5dy + (3 * dx + 3Y * dx) = 0
-1dx2y + 5dy + (3dx + 3dxY) = 0

Reorder the terms:
3dx + 3dxY + -1dx2y + 5dy = 0

Solving
3dx + 3dxY + -1dx2y + 5dy = 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(3x + 3xY + -1x2y + 5y) = 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 '(3x + 3xY + -1x2y + 5y)' equal to zero and attempt to solve:

Simplifying
3x + 3xY + -1x2y + 5y = 0

Solving
3x + 3xY + -1x2y + 5y = 0

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

Add '-3x' to each side of the equation.
3x + 3xY + -1x2y + -3x + 5y = 0 + -3x

Reorder the terms:
3x + -3x + 3xY + -1x2y + 5y = 0 + -3x

Combine like terms: 3x + -3x = 0
0 + 3xY + -1x2y + 5y = 0 + -3x
3xY + -1x2y + 5y = 0 + -3x
Remove the zero:
3xY + -1x2y + 5y = -3x

Add '-3xY' to each side of the equation.
3xY + -1x2y + -3xY + 5y = -3x + -3xY

Reorder the terms:
3xY + -3xY + -1x2y + 5y = -3x + -3xY

Combine like terms: 3xY + -3xY = 0
0 + -1x2y + 5y = -3x + -3xY
-1x2y + 5y = -3x + -3xY

Add 'x2y' to each side of the equation.
-1x2y + x2y + 5y = -3x + -3xY + x2y

Combine like terms: -1x2y + x2y = 0
0 + 5y = -3x + -3xY + x2y
5y = -3x + -3xY + x2y

Add '-5y' to each side of the equation.
5y + -5y = -3x + -3xY + x2y + -5y

Combine like terms: 5y + -5y = 0
0 = -3x + -3xY + x2y + -5y

Simplifying
0 = -3x + -3xY + x2y + -5y

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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