(Solved): - find laplace transformation of \( a-t \sin t \) \( b-t e^{-t} \sin t \) \( c-\frac{\sin t}{t} \) ...

- find laplace transformation of \( a-t \sin t \) \( b-t e^{-t} \sin t \) \( c-\frac{\sin t}{t} \) - find te solution using laplacian transformation: \[ y(t)-\int_{0}^{t} e^{t-\tau} y(t) d \tau=5 \] - using laplace method find the solution of: \[ \frac{\partial^{2} y(x, t)}{\partial x^{2}}-\frac{1}{v^{2}} \frac{\partial^{2} y(x, t)}{\partial t^{2}}=0 \] with intial condition \[ y(x, 0)=0,\left.\frac{\partial y}{\partial t}\right|_{t=0}=0 \]