(1X^4)dy+X(1+4y^2)dx=0

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Solution for (1X^4)dy+X(1+4y^2)dx=0 equation:


Simplifying
(1X4) * dy + X(1 + 4y2) * dx = 0

Remove parenthesis around (1X4)
1X4 * dy + X(1 + 4y2) * dx = 0

Multiply X4 * dy
1dyX4 + X(1 + 4y2) * dx = 0

Reorder the terms for easier multiplication:
1dyX4 + X * dx(1 + 4y2) = 0

Multiply X * dx
1dyX4 + dxX(1 + 4y2) = 0
1dyX4 + (1 * dxX + 4y2 * dxX) = 0
1dyX4 + (1dxX + 4dxy2X) = 0

Reorder the terms:
1dxX + 4dxy2X + 1dyX4 = 0

Solving
1dxX + 4dxy2X + 1dyX4 = 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), 'dX'.
dX(x + 4xy2 + yX3) = 0

Subproblem 1

Set the factor 'dX' equal to zero and attempt to solve: Simplifying dX = 0 Solving dX = 0 Move all terms containing d to the left, all other terms to the right. Simplifying dX = 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 '(x + 4xy2 + yX3)' equal to zero and attempt to solve: Simplifying x + 4xy2 + yX3 = 0 Solving x + 4xy2 + yX3 = 0 Move all terms containing d to the left, all other terms to the right. Add '-1x' to each side of the equation. x + 4xy2 + -1x + yX3 = 0 + -1x Reorder the terms: x + -1x + 4xy2 + yX3 = 0 + -1x Combine like terms: x + -1x = 0 0 + 4xy2 + yX3 = 0 + -1x 4xy2 + yX3 = 0 + -1x Remove the zero: 4xy2 + yX3 = -1x Add '-4xy2' to each side of the equation. 4xy2 + -4xy2 + yX3 = -1x + -4xy2 Combine like terms: 4xy2 + -4xy2 = 0 0 + yX3 = -1x + -4xy2 yX3 = -1x + -4xy2 Add '-1yX3' to each side of the equation. yX3 + -1yX3 = -1x + -4xy2 + -1yX3 Combine like terms: yX3 + -1yX3 = 0 0 = -1x + -4xy2 + -1yX3 Simplifying 0 = -1x + -4xy2 + -1yX3 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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