We found something rare

Hello Can anyone please help me and tell me if I have done the inverse laplace transform on this equation correctly? See attached word document

The sawtooth waveforms are used to control the horizontal and vertical motion of an electron beam that sweeps across the screen. The vertical deflection sawtooth waveform is responsible for moving the electron beam from the top of the screen to the bottom (this is known as trace) and back again...

Need to find laplace transform for L{exp(2t)/t}

Can anyone answer this problems using Laplace Transform and Partial Fraction Expansion? 1.) d^2x/dt^2 + 6dx/dt + 8x = 5sin3t 2.) d^2x/dt^2 + 8dx/dt + 25x = 10 u(t) 3.) d^2x/dt^2 + 2dx/dt + x = 5e^-2t Thanks.