use laplace transforms to solve ivp x" + 2x' - 15x = 6delta(t -9), x(0) =...
use laplace transforms to find ivp x"(t) + x(t) = g(t), x(0) = 3, x'(0) = -7
16. Solve the IVP with a Laplace transform method x" + 2x' + 2x = e-t, x(0) = 1, x'(0) = 1
solve using laplace transforms x" +0.4x' + 2x = 1 - Hz(t) x(0) =0, x'0) = 0
Q1: Use Laplace transforms to solve the initial value problem x" – 2x' + 5x = 1, 2(0) = 0, x'(0) = 0. 111. 7177J71111
use Laplace transforms to solve the given system of differential equations ponts) 6)) Use Laplace transforms to solve the system dc y = 2x-2y dt.dt dx _ ay = x - y dt at x(O) = 1, y(0) = 0
1) (20pts) Use the method of Laplace transforms to solve the IVP y" – 4y + 5y = 2e'; y(0) = 0, y(0) = 0 (You must use residues to compute the inverse transform to get full credit)
Detailed answer using the Laplace Transforms method Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i, where f(t)-〈0 otherwise. (b) z', +x-f(t), x(0) 0, z'(0)=1, where t/2 if 0 t< 6, 3 ift26 f(t) 3. Use Laplace transforms to solve the following initial value problems. Write the solution (t) for t20 as a simplified piecewise defined function. (a) z', + 2x' + 2x-f(t), x(0-0, z'(0)-i,...
5. Solve the following IVP by using the method of Laplace transforms: w"- 2 w' +w = 6 t - 2, w(-1) = 3 , w' ( -1) = 7
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