Modify the sample code above to venfy that $x(t)-\frac{1}{2}+C_e^{-e^2}$ is a family of solutions to the $1^{st}.$order differential equation $\frac{dx}{dt}+2tz-t.$ Plot the particular solutians for

the $3$ IVPS: $x(0)=\frac{3}{2}$;$x(0)=\frac{5}{2}$;$x(0)--\frac{1}{2}($you will neod to detorm ine the correct walues of $C$ that give these initial cond itions$).$ If recessary, adjust the parameters so

that the graphs are clearly displayed.

Put your modified code in cells below.

In Python, we use a double$-$asterisk $({?}^{****})$ to denote powrrs, not a caret $|||$ i