I want to find the solution $y_0(t)$ of the linear first-order ordinary differential equation
$$y'-(1/t)y= t \text{sin}(t)$$
satisfying the initial condition $y(\pi /2)=0$. I know how to do this analytically using the integrating factor and such, but how do I solve for this numerically (and what exactly does that mean anyway)?
Thanks for any input.