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Ankur posted an Question
April 06, 2021 • 14:52 pm 30 points
  • IIT JAM
  • Mathematics (MA)

19. let y be the solution of the initial value problem +y = 6 cos cos 2x, dx y(0) = 3, y (0) = 1 let the laplace transform of y be f(s),then the value of f(1) i

19. Let y be the solution of the initial value problem +y = 6 cos cos 2x, dx y(0) = 3, y (0) = 1 let the Laplace transform of y be F(s),Then the value of F(1) is 17 a b c)8 d)

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    Eduncle best-answer

    Hi ankur,kindly refer the below image for your query thank you for asking

    cropped545621074264539562.jpg
  • comment-profile-img>
    Ujjawal vishal

    Let L(y) = F(s) = Y then, L(y") = (s^2)Y - sy(0) - y'(0) = (s^2)Y - 3s - 1 & L(y') = sY - y(0) = sY - 1 also, L(cosax) = s/(s^2 + a^2) => L(cos2x) = s/(s^2 + 4) now taking Laplace transform of given differential equation and using above results , we get :- (s^2 + 1) Y - 3s - 1 = 6s/(s^2 + 4) => Y = 6s/[(s^2 + 4) (s^2 + 1)] + (3s + 1)/(s^2 + 1) hence , F(1) = Y(1) = 6/10 + 4/2 = 3/5 + 2 = 13/5

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    sir please provide solution on paper.🙏

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