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S_Student

  • 3 years ago

Can anyone solve it Laplace L(3t^2+3t^3+e^t+sin3t)

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  1. UnkleRhaukus
    • 3 years ago
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    \[\mathcal L\{3t^2+3t^3+e^t+\sin3t\}\]\[\qquad=3\mathcal L\{t^2\}+3\mathcal L\{t^3\}+\mathcal L\{e^t\}+\mathcal L\{\sin 3t\}\]

  2. UnkleRhaukus
    • 3 years ago
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    \[\boxed{\mathcal L\big\{t^n\big\}=\dfrac{\Gamma(n+1)}{s^{n+1}}}\qquad\boxed{\mathcal L\big\{e^{-at}\big\}=\dfrac{1}{s+a}}\qquad\boxed{\mathcal L \big\{\sin(bt) \big\}=\dfrac{b}{s^2+b^2}}\]

  3. S_Student
    • 3 years ago
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    thank you so much dear..

  4. UnkleRhaukus
    • 3 years ago
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    \[\color{teal} {\ddot\smile}\]

  5. S_Student
    • 3 years ago
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    can i ask one more question..?

  6. UnkleRhaukus
    • 3 years ago
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    yes

  7. S_Student
    • 3 years ago
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    ok thnx.. d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint

  8. UnkleRhaukus
    • 3 years ago
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    the laplace of?

  9. S_Student
    • 3 years ago
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    yup..

  10. UnkleRhaukus
    • 3 years ago
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    use \[\boxed{\mathcal L\big\{f'(t)\big\}=sF(s)-f(0)}\]\[\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\]

  11. hartnn
    • 3 years ago
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    since initial conditions are not given, assume them to be 0.

  12. UnkleRhaukus
    • 3 years ago
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    hmm, the question should state the initial conditions

  13. hartnn
    • 3 years ago
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    which gives you, \(\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)}\)

  14. hartnn
    • 3 years ago
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    when not given, we can safely assume then to be 0.

  15. UnkleRhaukus
    • 3 years ago
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    i wouldn't assume that, i would have initial conditions in my final result

  16. abb0t
    • 3 years ago
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    hmmm....verrrry interesting symbols ya'll got there.

  17. S_Student
    • 3 years ago
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    i dont understand :(

  18. Tushara
    • 3 years ago
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    do u have the initial conditions?

  19. S_Student
    • 3 years ago
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    yup

  20. Tushara
    • 3 years ago
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    please give them

  21. S_Student
    • 3 years ago
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    Laplace d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint

  22. Tushara
    • 3 years ago
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    there shud be more... r u give what y(0) is?

  23. hartnn
    • 3 years ago
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    dy/dt = f'(t) d^2y/dt^2 = f'' (t) d^3y/dt^3 = f'''(t) and then use, \(\boxed{\mathcal L\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\)

  24. Tushara
    • 3 years ago
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    given*

  25. S_Student
    • 3 years ago
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    DOnt know y(0) :(

  26. S_Student
    • 3 years ago
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    oh thnx hartnn

  27. S_Student
    • 3 years ago
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    i want thats,,step by step so thnx

  28. S_Student
    • 3 years ago
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    thanks to all who try to help me..

  29. Tushara
    • 3 years ago
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    i hope u can solve it now.... this might help, check out example 3: http://www2.fiu.edu/~aladrog/LaplaceTransDifferentialEq.pdf

  30. S_Student
    • 3 years ago
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    OK...thnx :)

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