(u^2*v^3+u+v-2)du+(u^3*v^2+u)dv=0

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Solution for (u^2*v^3+u+v-2)du+(u^3*v^2+u)dv=0 equation:


Simplifying
(u2 * v3 + u + v + -2) * du + (u3 * v2 + u) * dv = 0

Multiply u2 * v3
(u2v3 + u + v + -2) * du + (u3 * v2 + u) * dv = 0

Reorder the terms:
(-2 + u + u2v3 + v) * du + (u3 * v2 + u) * dv = 0

Reorder the terms for easier multiplication:
du(-2 + u + u2v3 + v) + (u3 * v2 + u) * dv = 0
(-2 * du + u * du + u2v3 * du + v * du) + (u3 * v2 + u) * dv = 0

Reorder the terms:
(-2du + duv + du2 + du3v3) + (u3 * v2 + u) * dv = 0
(-2du + duv + du2 + du3v3) + (u3 * v2 + u) * dv = 0

Multiply u3 * v2
-2du + duv + du2 + du3v3 + (u3v2 + u) * dv = 0

Reorder the terms:
-2du + duv + du2 + du3v3 + (u + u3v2) * dv = 0

Reorder the terms for easier multiplication:
-2du + duv + du2 + du3v3 + dv(u + u3v2) = 0
-2du + duv + du2 + du3v3 + (u * dv + u3v2 * dv) = 0
-2du + duv + du2 + du3v3 + (duv + du3v3) = 0

Reorder the terms:
-2du + duv + duv + du2 + du3v3 + du3v3 = 0

Combine like terms: duv + duv = 2duv
-2du + 2duv + du2 + du3v3 + du3v3 = 0

Combine like terms: du3v3 + du3v3 = 2du3v3
-2du + 2duv + du2 + 2du3v3 = 0

Solving
-2du + 2duv + du2 + 2du3v3 = 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), 'du'.
du(-2 + 2v + u + 2u2v3) = 0

Subproblem 1

Set the factor 'du' equal to zero and attempt to solve: Simplifying du = 0 Solving du = 0 Move all terms containing d to the left, all other terms to the right. Simplifying du = 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 '(-2 + 2v + u + 2u2v3)' equal to zero and attempt to solve: Simplifying -2 + 2v + u + 2u2v3 = 0 Reorder the terms: -2 + u + 2u2v3 + 2v = 0 Solving -2 + u + 2u2v3 + 2v = 0 Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + u + 2u2v3 + 2 + 2v = 0 + 2 Reorder the terms: -2 + 2 + u + 2u2v3 + 2v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + u + 2u2v3 + 2v = 0 + 2 u + 2u2v3 + 2v = 0 + 2 Combine like terms: 0 + 2 = 2 u + 2u2v3 + 2v = 2 Add '-1u' to each side of the equation. u + 2u2v3 + -1u + 2v = 2 + -1u Reorder the terms: u + -1u + 2u2v3 + 2v = 2 + -1u Combine like terms: u + -1u = 0 0 + 2u2v3 + 2v = 2 + -1u 2u2v3 + 2v = 2 + -1u Add '-2u2v3' to each side of the equation. 2u2v3 + -2u2v3 + 2v = 2 + -1u + -2u2v3 Combine like terms: 2u2v3 + -2u2v3 = 0 0 + 2v = 2 + -1u + -2u2v3 2v = 2 + -1u + -2u2v3 Add '-2v' to each side of the equation. 2v + -2v = 2 + -1u + -2u2v3 + -2v Combine like terms: 2v + -2v = 0 0 = 2 + -1u + -2u2v3 + -2v Simplifying 0 = 2 + -1u + -2u2v3 + -2v 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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