Just got these Homework questions and I needed help with them. show of work would help a lot. I will give thumbs up

1. Give the interval of existence for the solution for the initial value problem 10 pts (12-16)y"+ cos(41)y'=cset 1(5)= 1'(5) = 1"(5)= 0. 2. Suppose that Y (1), Y, (1), Y, (1) are solutions of the differential equation 10 pts y"- 3y"+(sint) y'+(13 +5)y=0. Suppose that W[Y , Y,, Y, ](0) =5. What is W[Y,, Y2, Y;](1) ? 3. The functions e2 and te2 are solutions of the differential equation 15 pts 10:11 PM V/ 3. The functions e2 and te2 are solutions of the differential equation 15 pts y"-4y'+4y=0. (a) Show they form a fundamental set of solutions. You don't have to check they are solutions. (b) Find the solution Y() to the general initial-value problem y"-4y'+4y=0, y(0)= yo' Y'(0) = y1 (c) Find the associated natural fundamental set of solutions to y"-4y'+ 4y=0 at time =0. 4. Find a general real solution of the equation 45 pts y"+25y=20e' +2cos(5t) +tsin(5t) +sec(5t). 10:12 PM J/ 5. The vertical displacement of a mass on a spring is given by 10 pts h"+6h'+13h= a cos(@t)+ Bsin(wt) where positive displacements are upward. (Assume a, B #0, @>0 . Assume CGS units.) (a) Is this system undamped, under damped, critically damped, or over damped? Explain why