$($ii$)y^{\text{'}\text{'}}+2y^{\text{'}}-3y=e^t,y(0)=1,y^{\text{'}}(0)=1.$

Exact solution: $y(t)=\frac{15}{16}{e}^t+\frac{1}{16}{e}^{-3t}+\frac{1}{4}t{e}^t.$

Hint: Convert second$-$order ordinary differential equation to a system of

first$-$order ordinary differential equations.

Write a java code for Runge Kutta of order $6$ to solve the above problem, Present the computed

approximate solutions along with their global errors with

step size, $h=0\mathrm{.}1,$tin$[0,1]$ in a table.