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Page 4 IV. (10) Use the Laplace transform to solve the IVP y" - 2y +...
Page 4 IV. Use the Laplace transform to solve the IVP y' - 2y + y = f(t), y(0) = 1, v/(0) = 1, where (10) 0, t <3 f(t) = t-3, 3 You may use the partial fraction decomposition 16–25+1) 5+(9–1 = (-) + ? + - , but you need to show all the steps needed to arrive to the expression - 022-28+1) in order to receive credit.
Page 4 IV. (10) Use the Laplace transform to solve the IVP y" - 2y + y = f(t), y(0) = 1, y(0) = 1, where t<5 f(t) = t-5, t5 You may use the partial fraction decomposition 7(x2–2x+1) (6-1) + + - , but you need to show all the steps needed to arrive to the expression -16-28+1) in order to receive credit. f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r", n=1,2,3,......
use the Laplace tronsform to solve the IVP Y"-2y + y = f(t), y(O) = 1, 4! (0)=/ Where 0, +23 f(+) { +-3, +23 2 you may use the portial fraction decompositron! +373 +7 - 27/1 3 30 (3.1)? S2(5²-25+1) 32(3-1/2 5-12 arrive to the expression: but show steps to 32 (57-25+1)
Page 2 II. (7) Use the Laplace Transform method to solve the IVP y' - 8y + 16y = 14 y(0) = 1,5/(0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y (s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the...
Page 2 T Use the Laplace Transform method to solve the IVP 1-8y + 16y-te (0) = 1,0) = 4 Show all your work. Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {v}(s), by first moving the expression of the form -as -b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y(8) which will be of...
Page 2 II. (7) Use the Laplace transform to solve the IVP y" - 5y' + 6y = 8(t-1), y(0) = 0,0) = 0, where the right hand side is the Dirac Delta Function (t - to) for to = 1. You may use the partial fraction decomposition 1 + 52-58 +6 2 S-3 but you need to show all the steps needed to arrive to the expression 1 52-58 +6 in order to receive credit. f(t)=L-'{F(s) Table of Laplace...
2. Use the Laplace Transform to solve the initial value problem y"-3y'+2y=h(t), y(O)=0, y'(0)=0, where h (t) = { 0,0<t<4 2, t>4
Use the Laplace Transform method to solve the IVP y" - 8y + 16y = t4 y(0) = 1,5(0) - 4. Show all your work Note: A partial fraction decomposition will not be needed here if you carefully solve for Y(s) = {y}(s), by first moving the expression of the form -as - b with a and b positive integers to the right hand side and then dividing both sides of the equation by the coefficient of Y() which will...
(t)= . Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3+), y(0) = 0, y(0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. L{y(t)}(s) b. Express the solution y(t) in terms of a...
IVP Use the Laplace Transform to solve the y"+y = f(t) y'ld-o, y(0)=0 where f(t) = { 1 Oste/ sint tz /