3ydx+(ct+5c)du=0

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Solution for 3ydx+(ct+5c)du=0 equation: 


Simplifying
3ydx + (ct + 5c) * du = 0

Reorder the terms:
3dxy + (5c + ct) * du = 0

Reorder the terms for easier multiplication:
3dxy + du(5c + ct) = 0
3dxy + (5c * du + ct * du) = 0

Reorder the terms:
3dxy + (cdtu + 5cdu) = 0
3dxy + (cdtu + 5cdu) = 0

Reorder the terms:
cdtu + 5cdu + 3dxy = 0

Solving
cdtu + 5cdu + 3dxy = 0

Solving for variable 'c'.

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

Add '-3dxy' to each side of the equation.
cdtu + 5cdu + 3dxy + -3dxy = 0 + -3dxy

Combine like terms: 3dxy + -3dxy = 0
cdtu + 5cdu + 0 = 0 + -3dxy
cdtu + 5cdu = 0 + -3dxy
Remove the zero:
cdtu + 5cdu = -3dxy

Combine like terms: -3dxy + 3dxy = 0
cdtu + 5cdu + 3dxy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(ctu + 5cu + 3xy) = 0


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

Simplifying
d = 0

Solving
d = 0

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

Add '-1d' to each side of the equation.
d + -1d = 0 + -1d
Remove the zero:
0 = -1d

Simplifying
0 = -1d

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 '(ctu + 5cu + 3xy)' equal to zero and attempt to solve:

Simplifying
ctu + 5cu + 3xy = 0

Solving
ctu + 5cu + 3xy = 0

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

Add '-3xy' to each side of the equation.
ctu + 5cu + 3xy + -3xy = 0 + -3xy

Combine like terms: 3xy + -3xy = 0
ctu + 5cu + 0 = 0 + -3xy
ctu + 5cu = 0 + -3xy
Remove the zero:
ctu + 5cu = -3xy

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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