In problems 1 to 7, solve all initial value problems. For each problem, state the largest interval in which the solution function is defined. 1. y"+y'=3e(1/2) y(0) = 4 y'(0) = 3 2. ty" -y=t+t y(1) = 1 y'(1) = 5 3. y" - y - 2y = 0 y(0) = 2 y'(0) = 7 4. (t? +9) y" + 2ty' = 0 y(3) = 2nt y'(3) = 2/3