How to solve a system of differential equations
x''[t] + t x'[t] + x[t] = z[t], y''[t] + y'[t] + y[t] = 0
and z''[t] + z'[t] +z[t] = 0 analytically using Mathematica?
{x[t],y[t],z[t]}/.FullSimplify[DSolve[ {x''[t]+t x'[t]+x[t]==z[t],y''[t]+y'[t]+y[t]==0,z''[t]+z'[t]+z[t]==0}, {x[t],y[t],z[t]},t]]
