Bessel function and equation problem

1. (15 points) Find an expression for J5/2(2) using properties of the Bessel function, given J3/2 () Sin T - COST 2. (5 points) Compute I(ex 1017 + 1) (e x 1017 - 1)! 3. (5 bonus points) Find an approximation for In Te x 10" ) good to one significant figure. You may wish to know that In 10 2 2.3 ~ 2, and e~ 2.71 83. 4. (10 points) Compute [ 5m Jm(I). 5. (30 points) Consider the differential equation zady