dy=(x+3y)dx

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Solution for dy=(x+3y)dx equation: 


Simplifying
dy = (x + 3y) * dx

Reorder the terms for easier multiplication:
dy = dx(x + 3y)
dy = (x * dx + 3y * dx)

Reorder the terms:
dy = (3dxy + dx2)
dy = (3dxy + dx2)

Solving
dy = 3dxy + dx2

Solving for variable 'd'.

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

Add '-3dxy' to each side of the equation.
-3dxy + dy = 3dxy + -3dxy + dx2

Combine like terms: 3dxy + -3dxy = 0
-3dxy + dy = 0 + dx2
-3dxy + dy = dx2

Add '-1dx2' to each side of the equation.
-3dxy + -1dx2 + dy = dx2 + -1dx2

Combine like terms: dx2 + -1dx2 = 0
-3dxy + -1dx2 + dy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(-3xy + -1x2 + y) = 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 '(-3xy + -1x2 + y)' equal to zero and attempt to solve:

Simplifying
-3xy + -1x2 + y = 0

Solving
-3xy + -1x2 + y = 0

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

Add '3xy' to each side of the equation.
-3xy + -1x2 + 3xy + y = 0 + 3xy

Reorder the terms:
-3xy + 3xy + -1x2 + y = 0 + 3xy

Combine like terms: -3xy + 3xy = 0
0 + -1x2 + y = 0 + 3xy
-1x2 + y = 0 + 3xy
Remove the zero:
-1x2 + y = 3xy

Add 'x2' to each side of the equation.
-1x2 + x2 + y = 3xy + x2

Combine like terms: -1x2 + x2 = 0
0 + y = 3xy + x2
y = 3xy + x2

Add '-1y' to each side of the equation.
y + -1y = 3xy + x2 + -1y

Combine like terms: y + -1y = 0
0 = 3xy + x2 + -1y

Simplifying
0 = 3xy + x2 + -1y

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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