dt(x+1)=ydx

Solution for dt(x+1)=ydx equation:

Simplifying
dt(x + 1) = ydx

Reorder the terms:
dt(1 + x) = ydx
(1 * dt + x * dt) = ydx
(1dt + dtx) = ydx

Solving
1dt + dtx = dxy

Solving for variable 'd'.

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

Add '-1dxy' to each side of the equation.
1dt + dtx + -1dxy = dxy + -1dxy

Combine like terms: dxy + -1dxy = 0
1dt + dtx + -1dxy = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(t + tx + -1xy) = 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 '(t + tx + -1xy)' equal to zero and attempt to solve:

Simplifying
t + tx + -1xy = 0

Solving
t + tx + -1xy = 0

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

Add '-1t' to each side of the equation.
t + tx + -1t + -1xy = 0 + -1t

Reorder the terms:
t + -1t + tx + -1xy = 0 + -1t

Combine like terms: t + -1t = 0
0 + tx + -1xy = 0 + -1t
tx + -1xy = 0 + -1t
Remove the zero:
tx + -1xy = -1t

Add '-1tx' to each side of the equation.
tx + -1tx + -1xy = -1t + -1tx

Combine like terms: tx + -1tx = 0
0 + -1xy = -1t + -1tx
-1xy = -1t + -1tx

Add 'xy' to each side of the equation.
-1xy + xy = -1t + -1tx + xy

Combine like terms: -1xy + xy = 0
0 = -1t + -1tx + xy

Simplifying
0 = -1t + -1tx + xy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}