Dy=(xy^2+3xy)dx

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Solution for Dy=(xy^2+3xy)dx equation: 


Simplifying
Dy = (xy2 + 3xy) * dx

Reorder the terms:
yD = (3xy + xy2) * dx

Reorder the terms for easier multiplication:
yD = dx(3xy + xy2)
yD = (3xy * dx + xy2 * dx)
yD = (3dx2y + dx2y2)

Solving
yD = 3dx2y + dx2y2

Solving for variable 'y'.

Reorder the terms:
-3dx2y + -1dx2y2 + yD = 3dx2y + dx2y2 + -3dx2y + -1dx2y2

Reorder the terms:
-3dx2y + -1dx2y2 + yD = 3dx2y + -3dx2y + dx2y2 + -1dx2y2

Combine like terms: 3dx2y + -3dx2y = 0
-3dx2y + -1dx2y2 + yD = 0 + dx2y2 + -1dx2y2
-3dx2y + -1dx2y2 + yD = dx2y2 + -1dx2y2

Combine like terms: dx2y2 + -1dx2y2 = 0
-3dx2y + -1dx2y2 + yD = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-3dx2 + -1dx2y + D) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-3dx2 + -1dx2y + D)' equal to zero and attempt to solve:

Simplifying
-3dx2 + -1dx2y + D = 0

Reorder the terms:
D + -3dx2 + -1dx2y = 0

Solving
D + -3dx2 + -1dx2y = 0

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

Add '-1D' to each side of the equation.
D + -3dx2 + -1D + -1dx2y = 0 + -1D

Reorder the terms:
D + -1D + -3dx2 + -1dx2y = 0 + -1D

Combine like terms: D + -1D = 0
0 + -3dx2 + -1dx2y = 0 + -1D
-3dx2 + -1dx2y = 0 + -1D
Remove the zero:
-3dx2 + -1dx2y = -1D

Add '3dx2' to each side of the equation.
-3dx2 + 3dx2 + -1dx2y = -1D + 3dx2

Combine like terms: -3dx2 + 3dx2 = 0
0 + -1dx2y = -1D + 3dx2
-1dx2y = -1D + 3dx2

Divide each side by '-1dx2'.
y = d-1x-2D + -3

Simplifying
y = d-1x-2D + -3

Reorder the terms:
y = -3 + d-1x-2D
Solution
y = {0, -3 + d-1x-2D}

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