Table of Laplace Transforms FunctionLaplace transforme−ats+a1sin(ωt)s2+ω2ωcos(ωt)s2+ω2stn,n≥0sn+1n!tp,p>1sp+1Γ(p+1)y′sy~(s)−y(0)y′′s2y~(s)−sy(0)−y′(0)