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

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


Simplifying
(2x + -3) * ydx + (y2 + -1x2 + 3x) * dy = 0

Reorder the terms:
(-3 + 2x) * ydx + (y2 + -1x2 + 3x) * dy = 0

Reorder the terms for easier multiplication:
dxy(-3 + 2x) + (y2 + -1x2 + 3x) * dy = 0
(-3 * dxy + 2x * dxy) + (y2 + -1x2 + 3x) * dy = 0
(-3dxy + 2dx2y) + (y2 + -1x2 + 3x) * dy = 0

Reorder the terms:
-3dxy + 2dx2y + (3x + -1x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
-3dxy + 2dx2y + dy(3x + -1x2 + y2) = 0
-3dxy + 2dx2y + (3x * dy + -1x2 * dy + y2 * dy) = 0
-3dxy + 2dx2y + (3dxy + -1dx2y + dy3) = 0

Reorder the terms:
-3dxy + 3dxy + 2dx2y + -1dx2y + dy3 = 0

Combine like terms: -3dxy + 3dxy = 0
0 + 2dx2y + -1dx2y + dy3 = 0
2dx2y + -1dx2y + dy3 = 0

Combine like terms: 2dx2y + -1dx2y = 1dx2y
1dx2y + dy3 = 0

Solving
1dx2y + dy3 = 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), 'dy'.
dy(x2 + y2) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 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 '(x2 + y2)' equal to zero and attempt to solve:

Simplifying
x2 + y2 = 0

Solving
x2 + y2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 + y2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
0 + y2 = 0 + -1x2
y2 = 0 + -1x2
Remove the zero:
y2 = -1x2

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

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

Simplifying
0 = -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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