Question

Solve this ordinary differential equation dy/dx = (x^2-x+)/(y-1)

Answer 1

This equation is easily separable as

`(\mathrm dy)/(\mathrm dx)=(x^2-x+k)/(y-1)\implies(y-1)\,\mathrm dy=(x^2-x+k)\,\mathrm dx`

where the
`k` term is assumed to be some constant that was omitted from the question. Integrating both sides gives

`\frac{y^2}2-y=\frac{x^3}3-\frac{x^2}2+kx+C`