anonymous
  • anonymous
Can anyone solve it Laplace L(3t^2+3t^3+e^t+sin3t)
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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UnkleRhaukus
  • UnkleRhaukus
\[\mathcal L\{3t^2+3t^3+e^t+\sin3t\}\]\[\qquad=3\mathcal L\{t^2\}+3\mathcal L\{t^3\}+\mathcal L\{e^t\}+\mathcal L\{\sin 3t\}\]
UnkleRhaukus
  • UnkleRhaukus
\[\boxed{\mathcal L\big\{t^n\big\}=\dfrac{\Gamma(n+1)}{s^{n+1}}}\qquad\boxed{\mathcal L\big\{e^{-at}\big\}=\dfrac{1}{s+a}}\qquad\boxed{\mathcal L \big\{\sin(bt) \big\}=\dfrac{b}{s^2+b^2}}\]
anonymous
  • anonymous
thank you so much dear..

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UnkleRhaukus
  • UnkleRhaukus
\[\color{teal} {\ddot\smile}\]
anonymous
  • anonymous
can i ask one more question..?
UnkleRhaukus
  • UnkleRhaukus
yes
anonymous
  • anonymous
ok thnx.. d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint
UnkleRhaukus
  • UnkleRhaukus
the laplace of?
anonymous
  • anonymous
yup..
UnkleRhaukus
  • UnkleRhaukus
use \[\boxed{\mathcal L\big\{f'(t)\big\}=sF(s)-f(0)}\]\[\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\]
hartnn
  • hartnn
since initial conditions are not given, assume them to be 0.
UnkleRhaukus
  • UnkleRhaukus
hmm, the question should state the initial conditions
hartnn
  • hartnn
which gives you, \(\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)}\)
hartnn
  • hartnn
when not given, we can safely assume then to be 0.
UnkleRhaukus
  • UnkleRhaukus
i wouldn't assume that, i would have initial conditions in my final result
abb0t
  • abb0t
hmmm....verrrry interesting symbols ya'll got there.
anonymous
  • anonymous
i dont understand :(
anonymous
  • anonymous
do u have the initial conditions?
anonymous
  • anonymous
yup
anonymous
  • anonymous
please give them
anonymous
  • anonymous
Laplace d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint
anonymous
  • anonymous
there shud be more... r u give what y(0) is?
hartnn
  • hartnn
dy/dt = f'(t) d^2y/dt^2 = f'' (t) d^3y/dt^3 = f'''(t) and then use, \(\boxed{\mathcal L\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\)
anonymous
  • anonymous
given*
anonymous
  • anonymous
DOnt know y(0) :(
anonymous
  • anonymous
oh thnx hartnn
anonymous
  • anonymous
i want thats,,step by step so thnx
anonymous
  • anonymous
thanks to all who try to help me..
anonymous
  • anonymous
i hope u can solve it now.... this might help, check out example 3: http://www2.fiu.edu/~aladrog/LaplaceTransDifferentialEq.pdf
anonymous
  • anonymous
OK...thnx :)

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