Find a particular solution to the ODE below using undetermined coefficients. Use t\displaystyle {t} as the independent variable.

y′′−2y′−3y=9t+24\displaystyle {y}{''}-{2}{y}'-{3}{y}={9}{t}+{24}

y(t)=\displaystyle {y}{\left({t}\right)}=  

Next, find the general solution to the ODE below. Use c1\displaystyle {c}_{{1}} and c2\displaystyle {c}_{{2}} as arbitrary constants

y(t)=\displaystyle {y}{\left({t}\right)}=  

Last, find the solution that satisfies the following initial conditions: y(0)=−12,y′(0)=−5\displaystyle {y}{\left({0}\right)}=-{12},\quad{y}'{\left({0}\right)}=-{5}

y(t)=\displaystyle {y}{\left({t}\right)}=  

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