I want to solve an ODE in the form \{y'[t] == f[y[t]], y[2] == \{1, 2, 3\}\} using NDSolve in Mathematica, where $f: R^3 \rightarrow R^3$ is defined as follows,
f[y_] := {2 y[[1]] + 1, 3 y[[2]] + y[[3]], 2 y[[3]] + y[[1]]} s = NDSolve[{y'[t] == f[y[t]], y[2] == {1, 2, 3}}, y, {t, 0, 10}] Plot[First[y /. s][t], {t, 0, 10}]
However, when I run the code it says "Part::partw: "Part 2 of y(t) does not exist."". How can I solve the problem?