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

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


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

Multiply xy * dy
dxy2 + (2x2 + 3y2 + -20) * dx = 0

Reorder the terms:
dxy2 + (-20 + 2x2 + 3y2) * dx = 0

Reorder the terms for easier multiplication:
dxy2 + dx(-20 + 2x2 + 3y2) = 0
dxy2 + (-20 * dx + 2x2 * dx + 3y2 * dx) = 0

Reorder the terms:
dxy2 + (-20dx + 3dxy2 + 2dx3) = 0
dxy2 + (-20dx + 3dxy2 + 2dx3) = 0

Reorder the terms:
-20dx + dxy2 + 3dxy2 + 2dx3 = 0

Combine like terms: dxy2 + 3dxy2 = 4dxy2
-20dx + 4dxy2 + 2dx3 = 0

Solving
-20dx + 4dxy2 + 2dx3 = 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), '2dx'.
2dx(-10 + 2y2 + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'dx' equal to zero and attempt to solve: Simplifying dx = 0 Solving dx = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx = 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 '(-10 + 2y2 + x2)' equal to zero and attempt to solve: Simplifying -10 + 2y2 + x2 = 0 Reorder the terms: -10 + x2 + 2y2 = 0 Solving -10 + x2 + 2y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '10' to each side of the equation. -10 + x2 + 10 + 2y2 = 0 + 10 Reorder the terms: -10 + 10 + x2 + 2y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x2 + 2y2 = 0 + 10 x2 + 2y2 = 0 + 10 Combine like terms: 0 + 10 = 10 x2 + 2y2 = 10 Add '-1x2' to each side of the equation. x2 + -1x2 + 2y2 = 10 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y2 = 10 + -1x2 2y2 = 10 + -1x2 Add '-2y2' to each side of the equation. 2y2 + -2y2 = 10 + -1x2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 0 = 10 + -1x2 + -2y2 Simplifying 0 = 10 + -1x2 + -2y2 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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