(3x+y)dx=(x+2y)dy

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Solution for (3x+y)dx=(x+2y)dy equation: 


Simplifying
(3x + y) * dx = (x + 2y) * dy

Reorder the terms for easier multiplication:
dx(3x + y) = (x + 2y) * dy
(3x * dx + y * dx) = (x + 2y) * dy

Reorder the terms:
(dxy + 3dx2) = (x + 2y) * dy
(dxy + 3dx2) = (x + 2y) * dy

Reorder the terms for easier multiplication:
dxy + 3dx2 = dy(x + 2y)
dxy + 3dx2 = (x * dy + 2y * dy)
dxy + 3dx2 = (dxy + 2dy2)

Add '-1dxy' to each side of the equation.
dxy + -1dxy + 3dx2 = dxy + -1dxy + 2dy2

Combine like terms: dxy + -1dxy = 0
0 + 3dx2 = dxy + -1dxy + 2dy2
3dx2 = dxy + -1dxy + 2dy2

Combine like terms: dxy + -1dxy = 0
3dx2 = 0 + 2dy2
3dx2 = 2dy2

Solving
3dx2 = 2dy2

Solving for variable 'd'.

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

Add '-2dy2' to each side of the equation.
3dx2 + -2dy2 = 2dy2 + -2dy2

Combine like terms: 2dy2 + -2dy2 = 0
3dx2 + -2dy2 = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(3x2 + -2y2) = 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 '(3x2 + -2y2)' equal to zero and attempt to solve:

Simplifying
3x2 + -2y2 = 0

Solving
3x2 + -2y2 = 0

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

Add '-3x2' to each side of the equation.
3x2 + -3x2 + -2y2 = 0 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 + -2y2 = 0 + -3x2
-2y2 = 0 + -3x2
Remove the zero:
-2y2 = -3x2

Add '2y2' to each side of the equation.
-2y2 + 2y2 = -3x2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
0 = -3x2 + 2y2

Simplifying
0 = -3x2 + 2y2

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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