Please feel free to ask any doubts regarding the solution.
Kind regards.
equations Ordinary Differential Homework problem 8 consider the initial value problem So if ostki - by...
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...
(1 point) Consider the initial value problem y' + 3y = 0 if 0 <t <3 9 if 3 < t < 5 0 if 5 <t< oo, y(0) = 3. (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). y(s)(5+6)...
So 0<t<5 Using the Laplace transform, solve the initial value problem y' + y = 3 t5 y'(0) = 0. 9
(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)
Consider the initial value problem O if 0 t<3 y+5y={11 if 3 <5 if 5 t00, y(0) = 10 (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). 11 A-3s)/5-11e-5s)/5+10 (S+5)Y (b) Solve your equation for Y Y =Lly) (c) Take...
(1 point) In this exercise we will use the Laplace transform to solve the following initial value problem: y-y={o. ist 1, 031<1. y(0) = 0 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation obtained by taking the Laplace transform of the initial value problem (2) Next solve for Y = (3) Finally apply the inverse Laplace transform to find y(t) y) = (1 point) Consider the initial value problem O +6y=...
Homework 16: Problem 3 Previous Problem Problem List Next Problem (1 point) Consider the initial value problem y" + 16y = 64t, y(0) = 9, y'(0) = 6. 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(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). help (formulas) b. Solve...
HW16: Problem 9 Previous Problem Problem List Next Problem (1 point) Consider the initial value problem o ifost <3 y + 5y = 10 if 3 st<5 3(0) = 4. lo if 5 <t< oo, (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...
(1 point) Consider the following initial value problem: y" + 36y= 0 <t< 5 t> 5 y(0) = 4, y'(0) = 0 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) =