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

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

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

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

y = - ln (- \frac{x ^{3}}{3} + x^{2} - x - c_{1})

Solution steps

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

Solve separable ODE:

y = - ln (- \frac{x ^{3}}{3} + x^{2} - x - c_{1})

y = - ln (- \frac{x ^{3}}{3} + x^{2} - x - c_{1})

y^{^{'}} + 2 y = - 10

e^{y} y^{^{'}} = \frac{( ln ( t ) ) ^{2}}{t}, y (1) = ln (2)

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

y^{^{'}} - 5 y = 0, y (0) = 2

\frac{d y}{d t} = y + 1, y (0) = 0

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