kooygi2830 kooygi2830
  • 20-09-2019
  • Mathematics
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Solve this ordinary differential equation dy/dx = (x^2-x+)/(y-1)

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LammettHash
LammettHash LammettHash
  • 04-02-2020

This equation is easily separable as

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^2-x+k}{y-1}\implies(y-1)\,\mathrm dy=(x^2-x+k)\,\mathrm dx[/tex]

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

[tex]\dfrac{y^2}2-y=\dfrac{x^3}3-\dfrac{x^2}2+kx+C[/tex]

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