What is the solution for (dy)/(dx)=(x+y-1)^3-1 ?

The solution for (dy)/(dx)=(x+y-1)^3-1 is y=sqrt(-1/(2(x+c_{1)))}-x+1,y=-sqrt(-1/(2(x+c_{1)))}-x+1

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(dy)/(dx)=(x+y-1)^3-1

\frac{d y}{d x} = (x + y - 1)^{3} - 1

y = - \frac{1}{2 ( x + c _{1} )} - x + 1, y = - - \frac{1}{2 ( x + c _{1} )} - x + 1

Solution steps

\frac{d y}{d x} = (x + y - 1)^{3} - 1

Solve using substitution:

y = - \frac{1}{2 ( x + c _{1} )} - x + 1, y = - - \frac{1}{2 ( x + c _{1} )} - x + 1

y = - \frac{1}{2 ( x + c _{1} )} - x + 1, y = - - \frac{1}{2 ( x + c _{1} )} - x + 1

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What is the solution for (dy)/(dx)=(x+y-1)^3-1 ?
The solution for (dy)/(dx)=(x+y-1)^3-1 is y=sqrt(-1/(2(x+c_{1)))}-x+1,y=-sqrt(-1/(2(x+c_{1)))}-x+1