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UnkleRhaukusBest ResponseYou've already chosen the best response.6
\[\mathcal L\{3t^2+3t^3+e^t+\sin3t\}\]\[\qquad=3\mathcal L\{t^2\}+3\mathcal L\{t^3\}+\mathcal L\{e^t\}+\mathcal L\{\sin 3t\}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.6
\[\boxed{\mathcal L\big\{t^n\big\}=\dfrac{\Gamma(n+1)}{s^{n+1}}}\qquad\boxed{\mathcal L\big\{e^{at}\big\}=\dfrac{1}{s+a}}\qquad\boxed{\mathcal L \big\{\sin(bt) \big\}=\dfrac{b}{s^2+b^2}}\]
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
thank you so much dear..
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.6
\[\color{teal} {\ddot\smile}\]
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
can i ask one more question..?
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
ok thnx.. d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.6
use \[\boxed{\mathcal L\big\{f'(t)\big\}=sF(s)f(0)}\]\[\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)s^{n1}f(0)s^{n2}f'(0)\dotssf^{n2}(0)f^{n1}(0)}\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
since initial conditions are not given, assume them to be 0.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.6
hmm, the question should state the initial conditions
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
which gives you, \(\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)}\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
when not given, we can safely assume then to be 0.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.6
i wouldn't assume that, i would have initial conditions in my final result
 one year ago

abb0tBest ResponseYou've already chosen the best response.0
hmmm....verrrry interesting symbols ya'll got there.
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
i dont understand :(
 one year ago

TusharaBest ResponseYou've already chosen the best response.0
do u have the initial conditions?
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
Laplace d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint
 one year ago

TusharaBest ResponseYou've already chosen the best response.0
there shud be more... r u give what y(0) is?
 one year ago

hartnnBest ResponseYou've already chosen the best response.0
dy/dt = f'(t) d^2y/dt^2 = f'' (t) d^3y/dt^3 = f'''(t) and then use, \(\boxed{\mathcal L\{f^n(t)\big\}=s^nF(s)s^{n1}f(0)s^{n2}f'(0)\dotssf^{n2}(0)f^{n1}(0)}\)
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
i want thats,,step by step so thnx
 one year ago

S_StudentBest ResponseYou've already chosen the best response.1
thanks to all who try to help me..
 one year ago

TusharaBest ResponseYou've already chosen the best response.0
i hope u can solve it now.... this might help, check out example 3: http://www2.fiu.edu/~aladrog/LaplaceTransDifferentialEq.pdf
 one year ago
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