Question

Use the Laplace transform to solve the following initial value problem: y'' + 9y' = 0 y(0) = 7, y'(0) = -4 a. 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 s^2Y - 7s + 4 + 9(sY - 7) = 0 b. Now solve for Y(s) = (7s + 59)/(s(9 + s)) c. Write the above answer in its partial fraction decomposition, Y(s) = A/(s+a) + B/(s+b) where a < b Y(s) = [ ] + [ ] d. Now by inverting the transform, find y(t) = 7 - 4/9 + 4/9e^{-9t}

          Use the Laplace transform to solve the following initial value problem:
y'' + 9y' = 0 y(0) = 7, y'(0) = -4
a. 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
s^2Y - 7s + 4 + 9(sY - 7) = 0
b. Now solve for
Y(s) = (7s + 59)/(s(9 + s))
c. Write the above answer in its partial fraction decomposition, Y(s) = A/(s+a) + B/(s+b) where a < b
Y(s) = [ ] + [ ]
d. Now by inverting the transform, find
y(t) = 7 - 4/9 + 4/9e^{-9t}

$Use the Laplace transform to solve the following initial value problem: y” + 9y' = 0 y(0) = 7, y'(0) = -4 a. Using Y for the Laplace transform of y(t), i.e., Y = Ly(t), find the equation you get by taking the Laplace transform of the differential equation s^2Y - 7s + 4 + 9(sY - 7) = 0 b. Now solve for Y(s) = (7s + 59)/(s(9 + s)) c. Write the above answer in its partial fraction decomposition, Y(s) = A/(s+a) + B/(s+b) where a < b Y(s) = [ ] + [ ] d. Now by inverting the transform, find y(t) = 7 - 4/9 + 4/9e^-9t$

Added by David B.

Question

Please give Ace some feedback