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  • Pregunta: Q7. Solve the initial value problems using Laplace Transform day a. 2 dt2 5 dy + 3y = 0, y(0) = 1, y'(0) = 1 - dt dạy b. + 2 dt2 dt + 5y = 0, y(0) = 0, y'(0) = 6 c. day dt2 848 + 16y = 0, y(0) = 2, y'(0) = 9 - dt d. 9 dạy dt2 e. dy + dt2 dt 12x + 4y = 121e-3t, y(0) = 10,y'(0) = 6 + 4y = 8t – 10,y(0) = 1, y'(0) = 7 292- y = 2y – 1, y(0) = 7,y'(0) = 2 f. 3 d²y

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    Hay 3 pasos para resolver este problema.
    Solución
    Paso 1

    (a). Solution:

    Given differential equation is

    2d2ydx2−5dydx+3y=0,y(0)=1,y′(0)=12y″−5y′+3y=0


    Explanation:

    Taking Laplacetransform on both sides,we get

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Texto de la transcripción de la imagen:
Q7. Solve the initial value problems using Laplace Transform day a. 2 dt2 5 dy + 3y = 0, y(0) = 1, y'(0) = 1 - dt dạy b. + 2 dt2 dt + 5y = 0, y(0) = 0, y'(0) = 6 c. day dt2 848 + 16y = 0, y(0) = 2, y'(0) = 9 - dt d. 9 dạy dt2 e. dy + dt2 dt 12x + 4y = 121e-3t, y(0) = 10,y'(0) = 6 + 4y = 8t – 10,y(0) = 1, y'(0) = 7 292- y = 2y – 1, y(0) = 7,y'(0) = 2 f. 3 d²y dt2 dt dy + 2 dt2 dt ty 4 cos 2t,y(0) = 0, y'(0) = 2 day h. dy -2e2t, y(0) = 0, y'(0) = 1 dt2 dt