Consider the following initial value problem. y" + 6y' + 34y = 8( - 1T) +...
Consider the initial value problem Remaining ume: 111.20 ( mm:sec 0 y' +6y= if 0 <t<1 if 1 <t < 5 if 5 <t<o, 10 0 y(0) = 8. (a) Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y by Y. Do not move any terms from one side of the equation to the other (until you get to part (b) below). (b) Solve your...
Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y = 8, 7(0) = 1, y'(O) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) y = 8 Find a linear differential operator that annihilates the function g(x) = 8. (Use D for the differential operator.) Solve the given initial-value problem. Y(X)...
(1 point) Use the Laplace transform to solve the following initial value problem: y" + 6y' - 16y = 0 y(0) = 3, y(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = C{y(t)). find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(S) = Y(s) = A. where a <b Now by...
(1 pt) Use the Laplace transform to solve the following initial value problem: y" +-6y' + 9y = 0 y0) = 2, y'(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, Y(s) = sta + Y(s) = 2 Now by inverting the...
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. Y" – 4y' + 4y = t3e2t, y(0) = 0, y'0) = 0 y(t) = 2016-2 Need Help? Read It Talk to a Tutor
Use the Laplace transform to solve the given initial-value problem. y'' + gy' s(t – 1), y(0) = 0, y'(0) = 1 y(t) ])+([ ]). 2(t- Need Help? Read It Master It Talk to a Tutor Submit Answer
Use the Laplace transform to solve the given initial-value problem. y" + 4y' + 29y = δ(t-a) + δ(t-3x), y(0) = 1, y"(0) = 0 y(t) = Need Help? Read ItTalik to a Tutor Use the Laplace transform to solve the given initial-value problem. y" + 4y' + 29y = δ(t-a) + δ(t-3x), y(0) = 1, y"(0) = 0 y(t) = Need Help? Read ItTalik to a Tutor
(1 point) Consider the following initial value problem: y" +9y (st, o<t<8 y(0) = 0, '(0) = 0 132, ?> 8 Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(8)
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)