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Simplifying 2x[3x + y + -1yexp(-1x2)] * dx + [x2 + 3y2 + exp(-1x2)] * dy = 0 Remove parenthesis around (-1x2) 2x[3x + y + -1epxy * -1x2] * dx + [x2 + 3y2 + exp(-1x2)] * dy = 0 Reorder the terms for easier multiplication: 2x[3x + y + -1 * -1epxy * x2] * dx + [x2 + 3y2 + exp(-1x2)] * dy = 0 Multiply -1 * -1 2x[3x + y + 1epxy * x2] * dx + [x2 + 3y2 + exp(-1x2)] * dy = 0 Multiply epxy * x2 2x[3x + y + 1epx3y] * dx + [x2 + 3y2 + exp(-1x2)] * dy = 0 Reorder the terms: 2x[1epx3y + 3x + y] * dx + [x2 + 3y2 + exp(-1x2)] * dy = 0 Reorder the terms for easier multiplication: 2x * dx[1epx3y + 3x + y] + [x2 + 3y2 + exp(-1x2)] * dy = 0 Multiply x * dx 2dx2[1epx3y + 3x + y] + [x2 + 3y2 + exp(-1x2)] * dy = 0 [1epx3y * 2dx2 + 3x * 2dx2 + y * 2dx2] + [x2 + 3y2 + exp(-1x2)] * dy = 0 Reorder the terms: [2depx5y + 2dx2y + 6dx3] + [x2 + 3y2 + exp(-1x2)] * dy = 0 [2depx5y + 2dx2y + 6dx3] + [x2 + 3y2 + exp(-1x2)] * dy = 0 Remove parenthesis around (-1x2) 2depx5y + 2dx2y + 6dx3 + [x2 + 3y2 + epx * -1x2] * dy = 0 Reorder the terms for easier multiplication: 2depx5y + 2dx2y + 6dx3 + [x2 + 3y2 + -1epx * x2] * dy = 0 Multiply epx * x2 2depx5y + 2dx2y + 6dx3 + [x2 + 3y2 + -1epx3] * dy = 0 Reorder the terms: 2depx5y + 2dx2y + 6dx3 + [-1epx3 + x2 + 3y2] * dy = 0 Reorder the terms for easier multiplication: 2depx5y + 2dx2y + 6dx3 + dy[-1epx3 + x2 + 3y2] = 0 2depx5y + 2dx2y + 6dx3 + [-1epx3 * dy + x2 * dy + 3y2 * dy] = 0 2depx5y + 2dx2y + 6dx3 + [-1depx3y + dx2y + 3dy3] = 0 Reorder the terms: -1depx3y + 2depx5y + 2dx2y + dx2y + 6dx3 + 3dy3 = 0 Combine like terms: 2dx2y + dx2y = 3dx2y -1depx3y + 2depx5y + 3dx2y + 6dx3 + 3dy3 = 0 Solving -1depx3y + 2depx5y + 3dx2y + 6dx3 + 3dy3 = 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), 'd'. d(-1epx3y + 2epx5y + 3x2y + 6x3 + 3y3) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(-1epx3y + 2epx5y + 3x2y + 6x3 + 3y3)' equal to zero and attempt to solve: Simplifying -1epx3y + 2epx5y + 3x2y + 6x3 + 3y3 = 0 Solving -1epx3y + 2epx5y + 3x2y + 6x3 + 3y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'epx3y' to each side of the equation. -1epx3y + 2epx5y + 3x2y + 6x3 + epx3y + 3y3 = 0 + epx3y Reorder the terms: -1epx3y + epx3y + 2epx5y + 3x2y + 6x3 + 3y3 = 0 + epx3y Combine like terms: -1epx3y + epx3y = 0 0 + 2epx5y + 3x2y + 6x3 + 3y3 = 0 + epx3y 2epx5y + 3x2y + 6x3 + 3y3 = 0 + epx3y Remove the zero: 2epx5y + 3x2y + 6x3 + 3y3 = epx3y Add '-2epx5y' to each side of the equation. 2epx5y + 3x2y + 6x3 + -2epx5y + 3y3 = epx3y + -2epx5y Reorder the terms: 2epx5y + -2epx5y + 3x2y + 6x3 + 3y3 = epx3y + -2epx5y Combine like terms: 2epx5y + -2epx5y = 0 0 + 3x2y + 6x3 + 3y3 = epx3y + -2epx5y 3x2y + 6x3 + 3y3 = epx3y + -2epx5y Add '-3x2y' to each side of the equation. 3x2y + 6x3 + -3x2y + 3y3 = epx3y + -2epx5y + -3x2y Reorder the terms: 3x2y + -3x2y + 6x3 + 3y3 = epx3y + -2epx5y + -3x2y Combine like terms: 3x2y + -3x2y = 0 0 + 6x3 + 3y3 = epx3y + -2epx5y + -3x2y 6x3 + 3y3 = epx3y + -2epx5y + -3x2y Add '-6x3' to each side of the equation. 6x3 + -6x3 + 3y3 = epx3y + -2epx5y + -3x2y + -6x3 Combine like terms: 6x3 + -6x3 = 0 0 + 3y3 = epx3y + -2epx5y + -3x2y + -6x3 3y3 = epx3y + -2epx5y + -3x2y + -6x3 Add '-3y3' to each side of the equation. 3y3 + -3y3 = epx3y + -2epx5y + -3x2y + -6x3 + -3y3 Combine like terms: 3y3 + -3y3 = 0 0 = epx3y + -2epx5y + -3x2y + -6x3 + -3y3 Simplifying 0 = epx3y + -2epx5y + -3x2y + -6x3 + -3y3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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