What is the solution for (dy)/(dx)=x^2y-3y+x^2-3 ?

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

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(dy)/(dx)=x^2y-3y+x^2-3

\frac{d y}{d x} = x^{2} y - 3 y + x^{2} - 3

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

Solution steps

\frac{d y}{d x} = x^{2} y - 3 y + x^{2} - 3

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{- 0.8}{cos ( y )}, y (0) = \frac{π}{3}

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

y^{^{'}} = \frac{x y ^{3}}{9}, y (0) = 6

x \frac{d y}{d x} = y + 3

x (x + 1) y^{^{'}} = y (y + 1)

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