y(0) = 6, y'(0) = 3 (1 point) Use the Laplace transform to solve the following initial value problem: y" - 5y' + 4y = 0,

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Y 0 6 Y 0 3 1 Point Use The Laplace Transform To Solve The Following Initial Value Problem Y 5y 4y 0 1 (30.08 KiB) Viewed 28 times

y(0) = 6, y'(0) = 3 (1 point) Use the Laplace transform to solve the following initial value problem: y" - 5y' + 4y = 0, (1) First, using Y for the Laplace transform of y(t), i.e., Y = C(y(t)), find the equation you get by taking the Laplace transform of the differential equation to obtain = 0 (2) Next solve for Y = (9/e^x)-(3/e (4x)) (3) Now write the above answer in its partial fraction form, Y = А + S a B 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) = -7e^(-t)+e (5)