Note: to find the solution of given initial value problem we use lapalce transform method.
Details explained in the image.
Q1: Use Laplace transforms to solve the initial value problem x" – 2x' + 5x =...
Use Laplace transforms to solve the following initial value problem. x"' + 6x' + 25x = 0; x(0) = 5, x'(0) = 6 Click the icon to view the table of Laplace transforms. X(t) = (Type an expression using t as the variable.)
Use Laplace transforms to solve the following initial value problem. x" + x = sin 8t, x(0) = 0, x'(0) = 0 Click the icon to view the table of Laplace transforms. The solution is x(t) = (Type an expression using t as the variable. Type an exact answer.)
Use Laplace transforms to solve the following initial value problem. X' + 2y' + x = 0, x'- y' + y = 0, x(0) = 0, y(0) = 400 Click the icon to view the table of Laplace transforms. The particular solution is x(t) = and y(t) = (Type an expression using t as the variable. Type an exact answer, using radicals as need
Use the method of Laplace transforms to solve the initial value problem for it dr-*+y. x(0) = 0,0) = 1
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
Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y" + y = f(t), y(0) - 1, 0) = 0, where - (1, osta 1/2 f(0) = sin(t), t2/2 . 70 y() = 1 (4- 7 )sin(e- 1 + cost- -cos( - ) Dale X Need Help? Read Watch Talk to a Tutor Submit Answer
Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y" + 25y = f(t), y(0) = 0, y (O) = 1, where RE) = {cos(5€), Ostan (Σπ rce) = f sin(51) + (t-1) -sin 5(t-T) 5 Jault- TE ) X
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,...
2. Use the methods of Laplace transforms to solve the initial value problem y" – yr e-t sin 2t, y(0) = 0, y'(O) = 0.
7.10.8 Use the method of Laplace transforms to solve the given initial value problem. Here, Dlx) and D[y] denote differentiation with respect to t x(0) = 5 D[x] +y = 0 16x + DIY] = 8 y(0) = 16 Click the icon to view information on Laplace transforms. x(t) = y(t) = (Type exact answers in terms of e.)