What is the solution for (dy)/(dx)=(y-1)^2x^3 ?

The solution for (dy)/(dx)=(y-1)^2x^3 is y=-4/(x^4+4c_{1)}+(x^4)/(x^4+4c_{1)}+(4c_{1})/(x^4+4c_{1)}

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(dy)/(dx)=(y-1)^2x^3

\frac{d y}{d x} = (y - 1)^{2} x^{3}

y = - \frac{4}{x ^{4} + 4 c _{1}} + \frac{x ^{4}}{x ^{4} + 4 c _{1}} + \frac{4 c _{1}}{x ^{4} + 4 c _{1}}

Solution steps

\frac{d y}{d x} = (y - 1)^{2} x^{3}

Solve separable ODE:

y = - \frac{4}{x ^{4} + 4 c _{1}} + \frac{x ^{4}}{x ^{4} + 4 c _{1}} + \frac{4 c _{1}}{x ^{4} + 4 c _{1}}

y = - \frac{4}{x ^{4} + 4 c _{1}} + \frac{x ^{4}}{x ^{4} + 4 c _{1}} + \frac{4 c _{1}}{x ^{4} + 4 c _{1}}

What is the solution for (dy)/(dx)=(y-1)^2x^3 ?
The solution for (dy)/(dx)=(y-1)^2x^3 is y=-4/(x^4+4c_{1)}+(x^4)/(x^4+4c_{1)}+(4c_{1})/(x^4+4c_{1)}