Question

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

Answer 1

\[\mathcal L\{3t^2+3t^3+e^t+\sin3t\}\]\[\qquad=3\mathcal L\{t^2\}+3\mathcal L\{t^3\}+\mathcal L\{e^t\}+\mathcal L\{\sin 3t\}\]

Answer 2

\[\boxed{\mathcal L\big\{t^n\big\}=\dfrac{\Gamma(n+1)}{s^{n+1}}}\qquad\boxed{\mathcal L\big\{e^{-at}\big\}=\dfrac{1}{s+a}}\qquad\boxed{\mathcal L \big\{\sin(bt) \big\}=\dfrac{b}{s^2+b^2}}\]

Answer 3

thank you so much dear..

Answer 4

\[\color{teal} {\ddot\smile}\]

Answer 5

can i ask one more question..?

Answer 6

yes

Answer 7

ok thnx..
d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint

Answer 8

the laplace of?

Answer 9

yup..

Answer 10

use
\[\boxed{\mathcal L\big\{f'(t)\big\}=sF(s)-f(0)}\]\[\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\]

Answer 11

since initial conditions are not given, assume them to be 0.

Answer 12

hmm, the question should state the initial conditions

Answer 13

which gives you,
\(\boxed{\mathcal L\big\{f^n(t)\big\}=s^nF(s)}\)

Answer 14

when not given, we can safely assume then to be 0.

Answer 15

i wouldn't assume that, i would have initial conditions in my final result

Answer 16

hmmm....verrrry interesting symbols ya'll got there.

Answer 17

i dont understand :(

Answer 18

do u have the initial conditions?

Answer 19

yup

Answer 20

please give them

Answer 21

Laplace d^3y/dt^3 + d^2y/dt^2 + dy/dt = sint

Answer 22

there shud be more... r u give what y(0) is?

Answer 23

dy/dt = f'(t)
d^2y/dt^2 = f'' (t)
d^3y/dt^3 = f'''(t)
and then use,
\(\boxed{\mathcal L\{f^n(t)\big\}=s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)\dots-sf^{n-2}(0)-f^{n-1}(0)}\)

Answer 24

given*

Answer 25

DOnt know y(0) :(

Answer 26

oh thnx hartnn

Answer 27

i want thats,,step by step
so thnx

Answer 28

thanks to all who try to help me..

Answer 29

i hope u can solve it now.... this might help, check out example 3: http://www2.fiu.edu/~aladrog/LaplaceTransDifferentialEq.pdf

Answer 30

OK...thnx :)