I need help for this Laplace transform problem! The table mentioned in ( ) is attached below the problem!

Use the Laplace transform to find all solution(s) of the IVP r' - ar = theat with r(0) = 0, where a is an arbitrary real constant and n is an arbitrary positive integer. For this question you may use either table of transforms on the next two pages without having to show the results in these tables (the first is a copy of the one from the Logan book, with typos fixed; the second is a picture of the table from the Boyce and Diprima book).I Ifg ] = 2 [f ] & [ a ] - NO ! I fcoaltest at = ( ). fete" It ) ( Sag(+)c- Stet ) Not true ! Short table of Laplace transforms (there's lots more, see table in Logan p. 175). f (t ) F(s) = [[f(t) ] = / f(t )e-st dt warning, in BED book : Last time eat 1 s - a - a=-5 use la instead of Ha n! tn sn+1' n = 0, 1, 2, 3, ... n=3 - & I+37 s (t - a) - as 3! 1 Ha = H(t - a) $ 3 +1 Su - 6 - as , a = 1 S K sinkt) $2 + K2 (K = 3 : R [sin ( 3+ ) ] = 3 5 2 + 9 S cos(kt) $2 + K2 H(t - a)f (t - a) e-as F(s) f (n) (t ) s" F(s) - sn-1f(0) - sn-2f'(0) -... - sof(n-1)(0) | f " ( + ) -hy s/ ( s ) - f (o ) 2. Using the table above, find the inverse Laplace transform of the following functions: last time. (a) 1 5+5/ So & s+ 5 ] = f (t ) - est (d) Page 3 of 5 $ 4 Page 4 of 5 ( meaning { LAN ] = = )