search
Log In
0 votes

If $f(t)$ is a function defined for all $t \geq 0$, its Laplace transform $F(s)$ is defined as

  1. $\int_{0}^{\infty }e^{st}f(t)dt \\$
  2. $\int_{0}^{\infty }e^{-st}f(t)dt \\$
  3. $\int_{0}^{\infty }e^{ist}f(t)dt \\$
  4. $\int_{0}^{\infty }e^{-ist}f(t)dt$
in Differential Equations 24.6k points
recategorized by

Please log in or register to answer this question.

Answer:

Related questions

0 votes
0 answers
Laplace transform of $\cos( \omega t)$ is $\dfrac{s}{s^2+\omega ^2} \\$ $\dfrac{\omega }{s^2+\omega ^2} \\$ $\dfrac{s}{s^2-\omega ^2} \\$ $\dfrac{\omega }{s^2-\omega ^2}$
asked Feb 24, 2017 in Differential Equations Arjun 24.6k points
0 votes
0 answers
Solutions of Laplace’s equation having continuous second-order partial derivatives are called biharmonic functions harmonic functions conjugate harmonic functions error functions
asked Feb 24, 2017 in Differential Equations Arjun 24.6k points
0 votes
1 answer
If the Laplace transform of a function $f(t)$ is given by $\frac{s+3}{\left ( s+1 \right )\left ( s+2 \right )}$, then $f(0)$ is $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$
asked Mar 1 in Differential Equations jothee 4.9k points
0 votes
0 answers
The solution of $\dfrac{d^2y}{dt^2}-y=1,$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is $\dfrac{1}{s(s+1)(s-1)} \\$ $\dfrac{1}{s(s+1)} \\$ $\dfrac{1}{s(s-1)} \\$ $\dfrac{1}{s-1} \\$
asked Sep 18, 2020 in Differential Equations jothee 4.9k points
0 votes
0 answers
The Laplace transform of $te^{t}$ is $\dfrac{s}{(s+1)^{2}} \\$ $\dfrac{1}{(s-1)^{2}} \\$ $\dfrac{1}{(s+1)^{2}} \\$ $\dfrac{s}{(s-1)}$
asked Feb 27, 2017 in Differential Equations Arjun 24.6k points
...