please help and show steps 3. Solve the following IVP: ly'(0) = y'o, y(0) = yo where p > 0 and k 1. 2. Let k=0 Use the above power series to solve the following IVP. List the first six nonzero terms the solution the differential equation. ay = (t + y)2 ,y(0) = 0.
Solve the initial value problem ry' + xy = 1, > 0 y(1) = 2.
wondering how to solve this using the Laplace transformation. thank you 6) 17pt) Solve the following IVP. y" +4y = f(t) y(O) = 0 ;'(0) = 0 if t <3 = (exp(0.2t) if t23
1. Assume G=< a>. Let beg. Prove that o(b) is a factor of o(a)
Solve y'' + 4y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 fort > 6
Solve the following initial value problem. St/2 if 0 <t<6 y" +y= 3 ift > 6 6 y(0) = y'(0) = 0 14Pm1011* 1917 Prid A++ V "Top14
6. Solve the following recurrence relations: (a) An+1 = 2 an , AO = 2 (b) n-1 An+1 =1+ ak , 0o = a1 = 1 ,n> 1 k=0
2. Solve the linear homogeneous IVP U+ rtuz = 0, u.1,0) = sinr, -o0<< 0, t> 0.
3. Let f : [0, 1] → R be uniformly continuous, so that for every e > 0, there exists >0 such that |x – y < =\f(x) – f(y)] < e for every x, y € [0, 1]. The graph of f is the set Gf = {(x, f(x)) : € [0, 1]}. Show that Gf has measure zero (9 points).
Solve the linear programming problem 91 minimize w = 40J1 + 3092 + 20J3 + 1094 + 1095 J1 +293 +44 > 300 subject to yi +42 +295 400 +244 +Js > 1000 91,..., J5 20 ΛΙΛΙ ΛΙ 292