use the Laplace tronsform to solve the IVP Y"-2y + y = f(t), y(O) = 1,...
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, 7(0) = 1, where t<3 f(t) = t-3, t3 You may use the partial fraction decomposition 70-28+1) -1,2 = (+*++* - , but you need to show all the steps needed to arrive to the expression (+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,......
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 /
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...
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...
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...
SOLVE #3 AND #4 PLEASE Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0 Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
Solve the IVP using laplace transformation y”+3y=(t-2)u(t-1) y(0)=-1 y’(0)=2 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1
1. (5 points) Use a Laplace transform to solve the initial value problem: y' + 2y + y = 21 +3, y(0) = 1,5 (0) = 0. 2. (5 points) Use a Laplace transform to solve the initial value problem: y + y = f(t), y(0) = 1, here f(0) = 2 sin(t) if 0 Str and f(0) = 0 otherwise.