Find the general solution to the Cauchy-Euler equation t2y10ty+28y=0\displaystyle {t}^{{2}}{y}{''}-{10}{t}{y}'+{28}{y}={0}. Use c1\displaystyle {c}_{{1}} and c2\displaystyle {c}_{{2}} as arbitrary constants.

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

Next, find the solution that satisfies the initial conditions y(1)=1,y(1)=2\displaystyle {y}{\left({1}\right)}=-{1},{y}'{\left({1}\right)}=-{2}.

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