Chapter 8.4, Problem 8P

Consider the initial value problem

$\begin{array}{ccc}x\text{'}\text{'}+t^{2}x\text{'}+3x=t;& x(0)=1,& x\text{'}(0)=2\end{array}$.

Convert this problem to a system of two first order equations, and determine approximate values of the solution at $t=0.5$ and $t=1.0$ using the Runge-Kutta method with $h=0.1$.