(xy)dx+(2x^2+3y^2-20)dy=0

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Solution for (xy)dx+(2x^2+3y^2-20)dy=0 equation: 


Simplifying
(xy) * dx + (2x2 + 3y2 + -20) * dy = 0

Multiply xy * dx
dx2y + (2x2 + 3y2 + -20) * dy = 0

Reorder the terms:
dx2y + (-20 + 2x2 + 3y2) * dy = 0

Reorder the terms for easier multiplication:
dx2y + dy(-20 + 2x2 + 3y2) = 0
dx2y + (-20 * dy + 2x2 * dy + 3y2 * dy) = 0

Reorder the terms:
dx2y + (2dx2y + -20dy + 3dy3) = 0
dx2y + (2dx2y + -20dy + 3dy3) = 0

Combine like terms: dx2y + 2dx2y = 3dx2y
3dx2y + -20dy + 3dy3 = 0

Solving
3dx2y + -20dy + 3dy3 = 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(3x2 + -20 + 3y2) = 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 '(3x2 + -20 + 3y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -20 + 3y2 = 0

Reorder the terms:
-20 + 3x2 + 3y2 = 0

Solving
-20 + 3x2 + 3y2 = 0

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

Add '20' to each side of the equation.
-20 + 3x2 + 20 + 3y2 = 0 + 20

Reorder the terms:
-20 + 20 + 3x2 + 3y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3x2 + 3y2 = 0 + 20
3x2 + 3y2 = 0 + 20

Combine like terms: 0 + 20 = 20
3x2 + 3y2 = 20

Add '-3x2' to each side of the equation.
3x2 + -3x2 + 3y2 = 20 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + 3y2 = 20 + -3x2
3y2 = 20 + -3x2

Add '-3y2' to each side of the equation.
3y2 + -3y2 = 20 + -3x2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
0 = 20 + -3x2 + -3y2

Simplifying
0 = 20 + -3x2 + -3y2

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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