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

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


Simplifying
y2dx + -1(2x2 + 3xy) * dy = 0

Reorder the terms:
dxy2 + -1(3xy + 2x2) * dy = 0

Reorder the terms for easier multiplication:
dxy2 + -1dy(3xy + 2x2) = 0
dxy2 + (3xy * -1dy + 2x2 * -1dy) = 0
dxy2 + (-3dxy2 + -2dx2y) = 0

Combine like terms: dxy2 + -3dxy2 = -2dxy2
-2dxy2 + -2dx2y = 0

Solving
-2dxy2 + -2dx2y = 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), '-2dxy'.
-2dxy(y + x) = 0

Ignore the factor -2.

Subproblem 1

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