This is my first time doing Laplace transform of derivatives and I'm not sure if my transform is correct.
The given expression is $$y^{''}+3y^{'} +2y=t$$ and the given values are $$y(0)=0, \space y^{'}(0)=2$$ What I got was $$S^2Y-0-2+3SY-3(0)+2Y=\frac{1}{s^2}$$ Then solving for $Y$ $$Y=\frac{1}{(S^2)(S^2+3S)}$$ Is my work correct?