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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

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