dy(y^2-y)=dx

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Solution for dy(y^2-y)=dx equation:


Simplifying
dy(y2 + -1y) = dx

Reorder the terms:
dy(-1y + y2) = dx
(-1y * dy + y2 * dy) = dx
(-1dy2 + dy3) = dx

Solving
-1dy2 + dy3 = dx

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-1dx' to each side of the equation.
-1dy2 + -1dx + dy3 = dx + -1dx

Reorder the terms:
-1dx + -1dy2 + dy3 = dx + -1dx

Combine like terms: dx + -1dx = 0
-1dx + -1dy2 + dy3 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + -1y2 + y3) = 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 '(-1x + -1y2 + y3)' equal to zero and attempt to solve: Simplifying -1x + -1y2 + y3 = 0 Solving -1x + -1y2 + y3 = 0 Move all terms containing d to the left, all other terms to the right. Add 'x' to each side of the equation. -1x + -1y2 + x + y3 = 0 + x Reorder the terms: -1x + x + -1y2 + y3 = 0 + x Combine like terms: -1x + x = 0 0 + -1y2 + y3 = 0 + x -1y2 + y3 = 0 + x Remove the zero: -1y2 + y3 = x Add 'y2' to each side of the equation. -1y2 + y2 + y3 = x + y2 Combine like terms: -1y2 + y2 = 0 0 + y3 = x + y2 y3 = x + y2 Add '-1y3' to each side of the equation. y3 + -1y3 = x + y2 + -1y3 Combine like terms: y3 + -1y3 = 0 0 = x + y2 + -1y3 Simplifying 0 = x + y2 + -1y3 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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