List of top Engineering Mathematics Questions on Laplace transforms asked in TS PGECET

Let \[ f(t)= \begin{cases} \sin t, & 0\le t\le \pi,\\ 0, & t>\pi. \end{cases} \] The Laplace transform of \(f(t)\) is
If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is
If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is
If \( \mathcal{L}\{f(t)\} = \frac{1 - e^{-1/s}}{s} \), then \( \mathcal{L}\{e^{-t}f(3t)\} \) is

If $L^{-1}\left\{\frac{e^{-\pi s}}{s^2+4s+5}\right\} = \begin{cases} 0, & t \le \pi \\ e^{a(t-\pi)}(f(t)), & t>\pi \end{cases}$, then $f(\pi/2)=$

The Laplace transform \( \mathcal{L}\{t^2 \sin 2t\} \) is
If \( \mathcal{L}(f(t)) = F(s) \), then \( \mathcal{L}((\cosh 2t)f(t)) \) is:
Laplace transform of \( \frac{e^{-at} - e^{-bt}}{t} \) is:
Using Laplace transformation, the value of $ \int_{0}^{\infty} \frac{\sin 2t}{t} dt $ is

If the Laplace transform of $ \int_0^t \frac{((1+2t)^2-1)e^{3t}}{t} dt = \frac{A}{S-3} + \frac{B}{(S-3)^2} + \frac{C}{(S-3)} $ then $3(A+B+C)=$