(3e^3t-2t)dt+e^3tdy=0

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Solution for (3e^3t-2t)dt+e^3tdy=0 equation: 


Simplifying
(3e3t + -2t) * dt + e3tdy = 0

Reorder the terms for easier multiplication:
dt(3e3t + -2t) + e3tdy = 0
(3e3t * dt + -2t * dt) + e3tdy = 0
(3de3t2 + -2dt2) + e3tdy = 0

Reorder the terms:
de3ty + 3de3t2 + -2dt2 = 0

Solving
de3ty + 3de3t2 + -2dt2 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'dt'.
dt(e3y + 3e3t + -2t) = 0


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

Simplifying
dt = 0

Solving
dt = 0

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

Simplifying
dt = 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 '(e3y + 3e3t + -2t)' equal to zero and attempt to solve:

Simplifying
e3y + 3e3t + -2t = 0

Reorder the terms:
3e3t + e3y + -2t = 0

Solving
3e3t + e3y + -2t = 0

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

Add '-3e3t' to each side of the equation.
3e3t + e3y + -3e3t + -2t = 0 + -3e3t

Reorder the terms:
3e3t + -3e3t + e3y + -2t = 0 + -3e3t

Combine like terms: 3e3t + -3e3t = 0
0 + e3y + -2t = 0 + -3e3t
e3y + -2t = 0 + -3e3t
Remove the zero:
e3y + -2t = -3e3t

Add '-1e3y' to each side of the equation.
e3y + -1e3y + -2t = -3e3t + -1e3y

Combine like terms: e3y + -1e3y = 0
0 + -2t = -3e3t + -1e3y
-2t = -3e3t + -1e3y

Add '2t' to each side of the equation.
-2t + 2t = -3e3t + -1e3y + 2t

Combine like terms: -2t + 2t = 0
0 = -3e3t + -1e3y + 2t

Simplifying
0 = -3e3t + -1e3y + 2t

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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