S_Student
Can anyone solve it
Laplace L(3t^2+3t^3+e^t+sin3t)
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UnkleRhaukus
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\[\mathcal L\{3t^2+3t^3+e^t+\sin3t\}\]\[\qquad=3\mathcal L\{t^2\}+3\mathcal L\{t^3\}+\mathcal L\{e^t\}+\mathcal L\{\sin 3t\}\]
UnkleRhaukus
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\[\boxed{\mathcal L\big\{t^n\big\}=\dfrac{\Gamma(n+1)}{s^{n+1}}}\qquad\boxed{\mathcal L\big\{e^{-at}\big\}=\dfrac{1}{s+a}}\qquad\boxed{\mathcal L \big\{\sin(bt) \big\}=\dfrac{b}{s^2+b^2}}\]
S_Student
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thank you so much dear..
UnkleRhaukus
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\[\color{teal} {\ddot\smile}\]
S_Student
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can i ask one more question..?
UnkleRhaukus
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yes
S_Student
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ok thnx..
d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint
UnkleRhaukus
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the laplace of?
S_Student
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yup..
UnkleRhaukus
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use
\[\boxed{\mathcal L\big\{f'(t)\big\}=sF(s)-f(0)}\]\[\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\]
hartnn
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since initial conditions are not given, assume them to be 0.
UnkleRhaukus
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hmm, the question should state the initial conditions
hartnn
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which gives you,
\(\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)}\)
hartnn
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when not given, we can safely assume then to be 0.
UnkleRhaukus
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i wouldn't assume that, i would have initial conditions in my final result
abb0t
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hmmm....verrrry interesting symbols ya'll got there.
S_Student
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i dont understand :(
Tushara
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do u have the initial conditions?
S_Student
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yup
Tushara
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please give them
S_Student
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Laplace d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint
Tushara
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there shud be more... r u give what y(0) is?
hartnn
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dy/dt = f'(t)
d^2y/dt^2 = f'' (t)
d^3y/dt^3 = f'''(t)
and then use,
\(\boxed{\mathcal L\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\)
Tushara
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given*
S_Student
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DOnt know y(0) :(
S_Student
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oh thnx hartnn
S_Student
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i want thats,,step by step
so thnx
S_Student
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thanks to all who try to help me..
S_Student
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OK...thnx :)