I go ahead and throw a bone on one of these.
\(\displaystyle \L\\y''-2y'-3y=1, \;\ y(0)=0, \;\ y'(0)=1\)
\(\displaystyle \L\\y''=p^{2}Y-py(0)-y'(0)\)
\(\displaystyle \L\\y'=pY-y(0)\)
\(\displaystyle \L\\p^{2}Y-py(0)-y'(0)-2(pY-y(0))-3Y=\frac{1}{p}\)
Now, solve for y, perform partial fractions on the right side and look up the inverse LaPlace in a table.
Can you see all of the lines?. Two are not displyaying correctly.