Question

Use the Laplace transform to solve the following initial value problem: y'' - y' = 0, y(0) = 3, y'(0) = 1 (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 to obtain = 0 (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, Y = A/(s - a) + B/(s - b) (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = + (4) Finally apply the inverse Laplace transform to find y(t) y(t) =

          Use the Laplace transform to solve the following initial value problem: y'' - y' = 0, y(0) = 3, y'(0) = 1
(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 to obtain
= 0
(2) Next solve for Y =
(3) Now write the above answer in its partial fraction form, Y = A/(s - a) + B/(s - b)
(NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1)
Y =
+
(4) Finally apply the inverse Laplace transform to find y(t)
y(t) =

$Use the Laplace transform to solve the following initial value problem: y” - y' = 0, y(0) = 3, y'(0) = 1 (1) First, using Y for the Laplace transform of y(t), i.e., Y = L(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, Y = A/(s - a) + B/(s - b) (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = + (4) Finally apply the inverse Laplace transform to find y(t) y(t) =$

Added by Karina E.

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