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

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

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

S_Student
 3 years ago
Best ResponseYou've already chosen the best response.1thank you so much dear..

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.6\[\color{teal} {\ddot\smile}\]

S_Student
 3 years ago
Best ResponseYou've already chosen the best response.1can i ask one more question..?

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

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0since initial conditions are not given, assume them to be 0.

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.6hmm, the question should state the initial conditions

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

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.0when not given, we can safely assume then to be 0.

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.6i wouldn't assume that, i would have initial conditions in my final result

abb0t
 3 years ago
Best ResponseYou've already chosen the best response.0hmmm....verrrry interesting symbols ya'll got there.

Tushara
 3 years ago
Best ResponseYou've already chosen the best response.0do u have the initial conditions?

S_Student
 3 years ago
Best ResponseYou've already chosen the best response.1Laplace d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint

Tushara
 3 years ago
Best ResponseYou've already chosen the best response.0there shud be more... r u give what y(0) is?

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

S_Student
 3 years ago
Best ResponseYou've already chosen the best response.1i want thats,,step by step so thnx

S_Student
 3 years ago
Best ResponseYou've already chosen the best response.1thanks to all who try to help me..

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