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Differential equation

I am currently having trouble with some of this stuff, and my job requires that i learn this all again so i was wondering if i could get some help

t(t-3)y''+2ty'-y=t^2
y(1)=yo, y'(1)=y1
y1 and yo are real constants
find the interval of the unique solution
Also find the interval if the above initial condition changes to y(4)=yo and y'(4)=y1

Find general solution using Euler-Cauchy Equation
3t^2y''+11ty'-3y=0
t>0

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