(9y^8+2(x^7)y)dx-(8x(y^7)+x^8)dy=0

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Solution for (9y^8+2(x^7)y)dx-(8x(y^7)+x^8)dy=0 equation:


Simplifying
(9y8 + 2(x7) * y) * dx + -1(8x(y7) + x8) * dy = 0

Multiply x7 * y
(9y8 + 2x7y) * dx + -1(8x(y7) + x8) * dy = 0

Reorder the terms:
(2x7y + 9y8) * dx + -1(8x(y7) + x8) * dy = 0

Reorder the terms for easier multiplication:
dx(2x7y + 9y8) + -1(8x(y7) + x8) * dy = 0
(2x7y * dx + 9y8 * dx) + -1(8x(y7) + x8) * dy = 0

Reorder the terms:
(9dxy8 + 2dx8y) + -1(8x(y7) + x8) * dy = 0
(9dxy8 + 2dx8y) + -1(8x(y7) + x8) * dy = 0

Multiply x * y7
9dxy8 + 2dx8y + -1(8xy7 + x8) * dy = 0

Reorder the terms for easier multiplication:
9dxy8 + 2dx8y + -1dy(8xy7 + x8) = 0
9dxy8 + 2dx8y + (8xy7 * -1dy + x8 * -1dy) = 0
9dxy8 + 2dx8y + (-8dxy8 + -1dx8y) = 0

Reorder the terms:
9dxy8 + -8dxy8 + 2dx8y + -1dx8y = 0

Combine like terms: 9dxy8 + -8dxy8 = 1dxy8
1dxy8 + 2dx8y + -1dx8y = 0

Combine like terms: 2dx8y + -1dx8y = 1dx8y
1dxy8 + 1dx8y = 0

Solving
1dxy8 + 1dx8y = 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), 'dxy'.
dxy(y7 + x7) = 0

Subproblem 1

Set the factor 'dxy' equal to zero and attempt to solve: Simplifying dxy = 0 Solving dxy = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dxy = 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 '(y7 + x7)' equal to zero and attempt to solve: Simplifying y7 + x7 = 0 Reorder the terms: x7 + y7 = 0 Solving x7 + y7 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x7' to each side of the equation. x7 + -1x7 + y7 = 0 + -1x7 Combine like terms: x7 + -1x7 = 0 0 + y7 = 0 + -1x7 y7 = 0 + -1x7 Remove the zero: y7 = -1x7 Add '-1y7' to each side of the equation. y7 + -1y7 = -1x7 + -1y7 Combine like terms: y7 + -1y7 = 0 0 = -1x7 + -1y7 Simplifying 0 = -1x7 + -1y7 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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