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

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


Simplifying
(x2 + -1y) * dx + (x2 + x) * dy = 0

Reorder the terms for easier multiplication:
dx(x2 + -1y) + (x2 + x) * dy = 0
(x2 * dx + -1y * dx) + (x2 + x) * dy = 0

Reorder the terms:
(-1dxy + dx3) + (x2 + x) * dy = 0
(-1dxy + dx3) + (x2 + x) * dy = 0

Reorder the terms:
-1dxy + dx3 + (x + x2) * dy = 0

Reorder the terms for easier multiplication:
-1dxy + dx3 + dy(x + x2) = 0
-1dxy + dx3 + (x * dy + x2 * dy) = 0
-1dxy + dx3 + (dxy + dx2y) = 0

Reorder the terms:
-1dxy + dxy + dx2y + dx3 = 0

Combine like terms: -1dxy + dxy = 0
0 + dx2y + dx3 = 0
dx2y + dx3 = 0

Solving
dx2y + dx3 = 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), 'dx2'.
dx2(y + x) = 0

Subproblem 1

Set the factor 'dx2' equal to zero and attempt to solve: Simplifying dx2 = 0 Solving dx2 = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dx2 = 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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