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HOMEWORK14: Problem 9 Previous Problem Problem List Next Problem (1 point) Use the Laplace transform to solve the following initial value problem: $y'' - 2y = 0$, y(0) = 2, y'(0) = -2 (1) First, using Y for the Laplace transform of y(t), i.e., $Y = \mathcal{L}\{y(t)\}$, find the equation you get by taking the Laplace transform of the differential equation to obtain $(s^2 - 2s)Y(s) + 2s - 6 = 0$ (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, $Y = \frac{A}{(s - a)} + \frac{B}{(s - b)}$ (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) =

          HOMEWORK14: Problem 9
Previous Problem Problem List Next Problem
(1 point)
Use the Laplace transform to solve the following initial value problem: $y'' - 2y = 0$,
y(0) = 2, y'(0) = -2
(1) First, using Y for the Laplace transform of y(t), i.e., $Y = \mathcal{L}\{y(t)\}$,
find the equation you get by taking the Laplace transform of the differential equation to obtain
$(s^2 - 2s)Y(s) + 2s - 6 = 0$
(2) Next solve for Y = 
(3) Now write the above answer in its partial fraction form, $Y = \frac{A}{(s - a)} + \frac{B}{(s - b)}$
(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) =

$HOMEWORK14: Problem 9 Previous Problem Problem List Next Problem (1 point) Use the Laplace transform to solve the following initial value problem: y” - 2y = 0, y(0) = 2, y'(0) = -2 (1) First, using Y for the Laplace transform of y(t), i.e., Y = ℒ{y(t)}, find the equation you get by taking the Laplace transform of the differential equation to obtain (s^2 - 2s)Y(s) + 2s - 6 = 0 (2) Next solve for Y = (3) Now write the above answer in its partial fraction form, Y = (A)/((s - a)) + (B)/((s - b)) (NOTE: the order that you enter your answers matter so you must order your terms so that the first corresponds to a and the second to b, where a < b. Also note, for example that -2 < 1) Y = (4) Finally apply the inverse Laplace transform to find y(t) y(t) =$

Added by Charles B.

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