In quantum mechanics. the study of the Schrodinger equation for the ease of a harmonic oscillator leads to a consideration of Hermite's equation. 3;\" 2h;r +1.1].r = Cl. where 1. is a parameter. Use the reduction of order formula to obtain an integral representation of a second linearly independent solution to Hermite's equation for the given value oil and corresponding solution t] in parts [a] and {b} below. c:) [a] r-.=r. 1=ltjr=3+rt2 2l1l=l:l [b] 3r. = 5. rm = s: + e3 F2ltl=l:l Find the general solutions to the following nonhomogeneous Cauchy-Euler equation using variation of parameters. tz"+ tz' + 36z = - tan (6 In (t)) What is a general solution to the corresponding homogeneous equation? Zh = (Use parentheses to clearly denote the argument of each function.) z(t) = (Use parentheses to clearly denote the argument of each function.)