(3y^2+10xy)dx+(y^2+x^2)dy=0

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Solution for (3y^2+10xy)dx+(y^2+x^2)dy=0 equation: 


Simplifying
(3y2 + 10xy) * dx + (y2 + x2) * dy = 0

Reorder the terms:
(10xy + 3y2) * dx + (y2 + x2) * dy = 0

Reorder the terms for easier multiplication:
dx(10xy + 3y2) + (y2 + x2) * dy = 0
(10xy * dx + 3y2 * dx) + (y2 + x2) * dy = 0

Reorder the terms:
(3dxy2 + 10dx2y) + (y2 + x2) * dy = 0
(3dxy2 + 10dx2y) + (y2 + x2) * dy = 0

Reorder the terms:
3dxy2 + 10dx2y + (x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
3dxy2 + 10dx2y + dy(x2 + y2) = 0
3dxy2 + 10dx2y + (x2 * dy + y2 * dy) = 0
3dxy2 + 10dx2y + (dx2y + dy3) = 0

Combine like terms: 10dx2y + dx2y = 11dx2y
3dxy2 + 11dx2y + dy3 = 0

Solving
3dxy2 + 11dx2y + 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(3xy + 11x2 + 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 '(3xy + 11x2 + y2)' equal to zero and attempt to solve:

Simplifying
3xy + 11x2 + y2 = 0

Solving
3xy + 11x2 + y2 = 0

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

Add '-3xy' to each side of the equation.
3xy + 11x2 + -3xy + y2 = 0 + -3xy

Reorder the terms:
3xy + -3xy + 11x2 + y2 = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
0 + 11x2 + y2 = 0 + -3xy
11x2 + y2 = 0 + -3xy
Remove the zero:
11x2 + y2 = -3xy

Add '-11x2' to each side of the equation.
11x2 + -11x2 + y2 = -3xy + -11x2

Combine like terms: 11x2 + -11x2 = 0
0 + y2 = -3xy + -11x2
y2 = -3xy + -11x2

Add '-1y2' to each side of the equation.
y2 + -1y2 = -3xy + -11x2 + -1y2

Combine like terms: y2 + -1y2 = 0
0 = -3xy + -11x2 + -1y2

Simplifying
0 = -3xy + -11x2 + -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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