Solve by D-Operator Method for the following set of simultaneous ODEs: dx/dt+ y − 2x = 0 dy/dt+ 3dx/dt+ 4y = 0 Given that x(0) =0 and y(0) = 1
a. With Laplace transformers solve x"+4x'+20x=0 ; x(0)=4 & x'(0)=-5 b. With Laplace transformers solve x'=2x+2y and y'=2x-y ; x(0)=1 & y(0)=2
Answer all of the following: Use Laplace transform to solve the following ODEs (show reasonable detail) j(t) + y(t) + 3y(t) = 0; y(0) = 1, y(0) = 2 (t) + (t) =t; (0) = 1, g(0) = -1
2. Solve each of these ODEs using power series method expanded around Xo = 0. Find the recurrence relation and use it to find the first FOUR terms in each of the two linearly independent solution. Express your answer in general form where possible (well, it is not always possible). (a) (25 marks) (x2 + 2)y” - xy + 4y = 2x - 1-47 Note: expressa in terms of power series. (b) 2x2y" + 3xy' + (2x - 1) =...
Solve without using laplace 2. X" + 2x' +10x = 0 x(0)=6, x'(0)=3
solve using laplace transforms x" +0.4x' + 2x = 1 - Hz(t) x(0) =0, x'0) = 0
(a),(c),(d) Problems 18 Solve the following ODEs using Laplace transforms: (a) + 23(t) _ у(t) _ 2y(t)' 0 given y(0) y(0) 0 and у(0) (b) y(t) + 43(t) + 4y(t)-v-t given y(0)-У(0) -0 (c) j;(t)-2ý(t) + y(t)--e2t given y(0) ,(0) -1 (d) a)+2) y) 3e-given y(0) 4,(0) 2 (e) y(t) + 2ý(t) + 2y(1) 5 sin t given y(0)-У(0)-: 0 (f) y(t) + 6)() + 9y(t) -121-e_3r given y(0) у(0) 0 6 Problems 18 Solve the following ODEs using Laplace...
10) 3. Solve the following initial value problems using Laplace transforms. [(a)] (a) x." - 2x + 2x = e..(0) = 0, /'(0) = 1 (b)" - r = 8(t)..(0) = (0) = 0 (20
16. Solve the IVP with a Laplace transform method x" + 2x' + 2x = e-t, x(0) = 1, x'(0) = 1
use laplace transforms to solve ivp x" + 2x' - 15x = 6delta(t -9), x(0) = -5, x'(0) = 7