Fill in the blanks. $1+1 SO s+371 To S+1 5+2 Example 1: Find the solution to...
fill in the blanks. b a d (s+1) S-1 5+1 st-2s +1 Example 3: Find the solution to the 4th order IVP y'' - 2y" + y = 0, y(0) = 1, y'0) = -1, y"0) = 0, and y'" (0)=2. Solution: Step 1: Take the LT of this IVP: (s*Y(s) - sy(0) - say'(0) - sy"(0) - y" (0)) - 2 (s2Y(s) - sy(0) - y'(0)) + Y($) = 0 so (s* – 252 + 1)Y(s) – 53 +52...
evens from 2 and 6 In Exercises 1-6 find a particular solution by the method used in Example 5.3.2. Then find the general solution and, where indicated, solve the initial value problem and graph the solution. 1. y' + 5y - 6y= 22 + 180 - 1842 2. y' - 4y + 5y = 1+ 5.0 3. y' + 8y + 7y = -8-2+24x2 + 7ar3 4. y' - 4y + 4y = 2 + 8x - 4.2 CIG /'...
Just do the green circle For Exercises 67-74, factor out the polynomial CLI.S 67 y(a 3) 2(a 3) GC Set 69.ja(an卞sn) + b(2h (2m+3m)(4a+b)3 68. a(x - 4) +5(x -4) (x 4a+5) a-3)y +2) 72. 3m(3a-2)- 4(3a 2 1)5x(4m-5)-2(4m-5) (3a 2)(3m -4) 70. 3m(3a +5b) +n(3a + 5b) 3a+56)(3m+) 4-5)(5x 2) 74. 6r(3y +5) -3a(3y +5) (3y+52)21-) Objective 4 Prep Exercise 5 What kinds of polynomials are factored by grouping? Four-term polynomials Prep Exercise 6 When factoring by grouping, after...
2a,2b, and 2c 1. Assuming x > 0, find the general solution of the following Euler equa- tions. f) 5x2y" +12xy' +2y = 0 g) 2y"xy 0 h) a2y" - 2xy =0 i) a2y"-ay-n(n + 2)y 0, where n is a positive integer a) x2y"-3ay 4y 0 b) x2y"-5ay +10y 0 c) 6x2y" +7xy - y 0 d) xy"y0 e) x2y"-3ay' +13y 0 2. Find the solution of the following problems. Before doing these prob- lems, you might want to...
Question 1: [25 pts] S+1 a) Find the inverse Laplace transform of the expression $2+4 b) Find the inverse Laplace transform of the expression (s-5)(s2+4) c) Use the information from the parts a) and b) to find the solution of the IVP y" + 4y = 6e5t, y(0) = 1, y'(0) = 1.
completeness and clarity 2. Find a particular solution for the IVP y" - 2y + 2y = 8(t - 5), y(0) = 0, y0) = 1
Problem 2: [Also challenging] Find the solution of the following IVP: y' +2y = g(t), with y(0) = 3 where g(t) = - 0<t<1: g(t) = te-2 > 1.
29&30 please 3 -23 4 3-2 25. 3 4926. |0 1 1 0 0-2 1 2-5 Finding a Basis In Exercises 27-30, find a basis B for the domain of T such that the matrix for T relative to B is diagonal. 27. T: R2→R-T(x, y) = (x + y, x + y) 28. T: R3→R, Tu, y, z) (-2x +2y -3z, 2r y -6z. 2y) a + (af+ 2b)s 29. T: Pi-Pi T(a + bx) 30. T: P㈠Pg Tle...
1) Graph the solution curve from [0,5] with step .1 2) Find the explicit solution of the IVP 3) Find the interval of definition Consider the initial-value problem y" + x(y')2 = 0, y(1) = 4, y'(1) = 2
2. Use the Laplace transform to find a particular solution of the differen- tial equation (as explained in Example 2). After that, find the solution of the IVP. a) y"+y - 2y = 3t, y(0) = 0, '0) = 1 b) y" +4y=t, y(0) = 1, y(0) = 0