A community for students.
Here's the question you clicked on:
 0 viewing
S_Student
 2 years ago
Can anyone solve it
Laplace L(3t^2+3t^3+e^t+sin3t)
S_Student
 2 years ago
Can anyone solve it Laplace L(3t^2+3t^3+e^t+sin3t)

This Question is Open

UnkleRhaukus
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1thank you so much dear..

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

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

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

UnkleRhaukus
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0since initial conditions are not given, assume them to be 0.

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

hartnn
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0when not given, we can safely assume then to be 0.

UnkleRhaukus
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.0hmmm....verrrry interesting symbols ya'll got there.

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

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

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

hartnn
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1i want thats,,step by step so thnx

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

Tushara
 2 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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.