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

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

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

\frac{d y}{d x} = x^{2} y - y + x^{2} - 1

y = e^{\frac{x ^{3}}{3} - x + c_{1}} - 1

Solution steps

\frac{d y}{d x} = x^{2} y - y + x^{2} - 1

Solve separable ODE:

y = e^{\frac{x ^{3}}{3} - x + c_{1}} - 1

y = e^{\frac{x ^{3}}{3} - x + c_{1}} - 1

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