(72x^2-14x)dx-dy=0

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Solution for (72x^2-14x)dx-dy=0 equation:


Simplifying
(72x2 + -14x) * dx + -1dy = 0

Reorder the terms:
(-14x + 72x2) * dx + -1dy = 0

Reorder the terms for easier multiplication:
dx(-14x + 72x2) + -1dy = 0
(-14x * dx + 72x2 * dx) + -1dy = 0
(-14dx2 + 72dx3) + -1dy = 0

Solving
-14dx2 + 72dx3 + -1dy = 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(-14x2 + 72x3 + -1y) = 0

Subproblem 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 = 0

Subproblem 2

Set the factor '(-14x2 + 72x3 + -1y)' equal to zero and attempt to solve: Simplifying -14x2 + 72x3 + -1y = 0 Solving -14x2 + 72x3 + -1y = 0 Move all terms containing d to the left, all other terms to the right. Add '14x2' to each side of the equation. -14x2 + 72x3 + 14x2 + -1y = 0 + 14x2 Reorder the terms: -14x2 + 14x2 + 72x3 + -1y = 0 + 14x2 Combine like terms: -14x2 + 14x2 = 0 0 + 72x3 + -1y = 0 + 14x2 72x3 + -1y = 0 + 14x2 Remove the zero: 72x3 + -1y = 14x2 Add '-72x3' to each side of the equation. 72x3 + -72x3 + -1y = 14x2 + -72x3 Combine like terms: 72x3 + -72x3 = 0 0 + -1y = 14x2 + -72x3 -1y = 14x2 + -72x3 Add 'y' to each side of the equation. -1y + y = 14x2 + -72x3 + y Combine like terms: -1y + y = 0 0 = 14x2 + -72x3 + y Simplifying 0 = 14x2 + -72x3 + y 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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