What is the solution for (dx)/(dt)=tx-2x+t-2 ?

The solution for (dx)/(dt)=tx-2x+t-2 is x=e^{(t^2)/2-2t+c_{1}}-1

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(dx)/(dt)=tx-2x+t-2

\frac{d x}{d t} = t x - 2 x + t - 2

x = e^{\frac{t ^{2}}{2} - 2 t + c_{1}} - 1

Solution steps

\frac{d x}{d t} = t x - 2 x + t - 2

Solve separable ODE:

x = e^{\frac{t ^{2}}{2} - 2 t + c_{1}} - 1

x = e^{\frac{t ^{2}}{2} - 2 t + c_{1}} - 1

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What is the solution for (dx)/(dt)=tx-2x+t-2 ?
The solution for (dx)/(dt)=tx-2x+t-2 is x=e^{(t^2)/2-2t+c_{1}}-1