Ordinary Differential Equations and Initial-Value Problems : Unique Solution

Find the unique solution satisfying initial conditions y(1)=0 and y'(1)=1 for
ty''-(t+2)y'=2y=0, t not equal to 0


Solve t^2y''+3ty'+5y=0


Solve the initial value problem.
y''-2y'+y=2e^t+3
y(0)=4 and y'(0)=3