A programmable calculator or a computer will be useful for this problem. Find the exact solution of the given initial

value problem. Then apply the improved Euler method twice to approximate this solution on the given interval, first

with step size $h=0\mathrm{.}01,$ then with step size $h=0\mathrm{.}005.$ Make a table showing the approximate values and the

actual values, together with the percentage error in the more accurate approximations, for $x$ an integral multiple of

$0\mathrm{.}2.$

$y^{\text{'}}=y-3,y(0)=2$;$0x1$

Find the exact solution of the given initial value problem.

$y(x)=$