(xy)dx+(x^2+y^2)dy=0

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


Simplifying
(xy) * dx + (x2 + y2) * dy = 0

Multiply xy * dx
dx2y + (x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
dx2y + dy(x2 + y2) = 0
dx2y + (x2 * dy + y2 * dy) = 0
dx2y + (dx2y + dy3) = 0

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

Solving
2dx2y + 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(2x2 + 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 '(2x2 + y2)' equal to zero and attempt to solve:

Simplifying
2x2 + y2 = 0

Solving
2x2 + y2 = 0

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

Add '-2x2' to each side of the equation.
2x2 + -2x2 + y2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0 + y2 = 0 + -2x2
y2 = 0 + -2x2
Remove the zero:
y2 = -2x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -2x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -2x2 + -1y2

Simplifying
0 = -2x2 + -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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