ydx-(y^2-x^2)dy=0

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Solution for ydx-(y^2-x^2)dy=0 equation:


Simplifying
ydx + -1(y2 + -1x2) * dy = 0

Reorder the terms:
dxy + -1(-1x2 + y2) * dy = 0

Reorder the terms for easier multiplication:
dxy + -1dy(-1x2 + y2) = 0
dxy + (-1x2 * -1dy + y2 * -1dy) = 0
dxy + (1dx2y + -1dy3) = 0

Solving
dxy + 1dx2y + -1dy3 = 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(x + x2 + -1y2) = 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 '(x + x2 + -1y2)' equal to zero and attempt to solve: Simplifying x + x2 + -1y2 = 0 Solving x + x2 + -1y2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + x2 + -1x + -1y2 = 0 + -1x Reorder the terms: x + -1x + x2 + -1y2 = 0 + -1x Combine like terms: x + -1x = 0 0 + x2 + -1y2 = 0 + -1x x2 + -1y2 = 0 + -1x Remove the zero: x2 + -1y2 = -1x Add '-1x2' to each side of the equation. x2 + -1x2 + -1y2 = -1x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1y2 = -1x + -1x2 -1y2 = -1x + -1x2 Add 'y2' to each side of the equation. -1y2 + y2 = -1x + -1x2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -1x + -1x2 + y2 Simplifying 0 = -1x + -1x2 + y2 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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