(10+6y+(e^3x))dx(-2)dy=0

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Solution for (10+6y+(e^3x))dx(-2)dy=0 equation:


Simplifying
(10 + 6y + (e3x)) * dx(-2) * dy = 0
(10 + 6y + e3x) * dx(-2) * dy = 0

Reorder the terms:
(10 + e3x + 6y) * dx(-2) * dy = 0

Reorder the terms for easier multiplication:
-2dx * dy(10 + e3x + 6y) = 0

Multiply dx * dy
-2d2xy(10 + e3x + 6y) = 0
(10 * -2d2xy + e3x * -2d2xy + 6y * -2d2xy) = 0

Reorder the terms:
(-2d2e3x2y + -20d2xy + -12d2xy2) = 0
(-2d2e3x2y + -20d2xy + -12d2xy2) = 0

Solving
-2d2e3x2y + -20d2xy + -12d2xy2 = 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), '-2d2xy'.
-2d2xy(e3x + 10 + 6y) = 0

Ignore the factor -2.

Subproblem 1

Set the factor 'd2xy' equal to zero and attempt to solve: Simplifying d2xy = 0 Solving d2xy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d2xy = 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 '(e3x + 10 + 6y)' equal to zero and attempt to solve: Simplifying e3x + 10 + 6y = 0 Reorder the terms: 10 + e3x + 6y = 0 Solving 10 + e3x + 6y = 0 Move all terms containing d to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + e3x + -10 + 6y = 0 + -10 Reorder the terms: 10 + -10 + e3x + 6y = 0 + -10 Combine like terms: 10 + -10 = 0 0 + e3x + 6y = 0 + -10 e3x + 6y = 0 + -10 Combine like terms: 0 + -10 = -10 e3x + 6y = -10 Add '-1e3x' to each side of the equation. e3x + -1e3x + 6y = -10 + -1e3x Combine like terms: e3x + -1e3x = 0 0 + 6y = -10 + -1e3x 6y = -10 + -1e3x Add '-6y' to each side of the equation. 6y + -6y = -10 + -1e3x + -6y Combine like terms: 6y + -6y = 0 0 = -10 + -1e3x + -6y Simplifying 0 = -10 + -1e3x + -6y 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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