ln(y)dy=3xy*dx

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Solution for ln(y)dy=3xy*dx equation: 


Simplifying
ln(y) * dy = 3xy * dx

Multiply ln * y
lny * dy = 3xy * dx

Multiply lny * dy
dlny2 = 3xy * dx

Multiply xy * dx
dlny2 = 3dx2y

Solving
dlny2 = 3dx2y

Solving for variable 'd'.

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

Add '-3dx2y' to each side of the equation.
dlny2 + -3dx2y = 3dx2y + -3dx2y

Combine like terms: 3dx2y + -3dx2y = 0
dlny2 + -3dx2y = 0

Factor out the Greatest Common Factor (GCF), 'dy'.
dy(lny + -3x2) = 0


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

Simplifying
dy = 0

Solving
dy = 0

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

Simplifying
dy = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(lny + -3x2)' equal to zero and attempt to solve:

Simplifying
lny + -3x2 = 0

Solving
lny + -3x2 = 0

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

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

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

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

Combine like terms: -3x2 + 3x2 = 0
0 = -1lny + 3x2

Simplifying
0 = -1lny + 3x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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