NDSolve::pdord
NDSolveValue::pdord
ParametricNDSolve::pdord
ParametricNDSolveValue::pdord
A warning message is generated because there are no derivatives of y[t] in the equations:
NDSolve[{x'[t] == 2 y[t], x'[t] == 1 - y[t], x[0] == 1}, {x, y}, {t, 0, 1}]Here, λ[t] appears with no derivative. Therefore, the equations will be solved as a differential-algebraic equation. The message is just a warning:
eqns = {x''[t] + λ[t] x[t] == 0, y''[t] + λ[t] y[t] == -1, D[x[t] ^ 2 + y[t] ^ 2 == 1, {t, 2}]};
conds = {x[0] == 1, x'[0] == 0, x''[0] == 0, y[0] == 0, y'[0] == 0, y''[0] == -1, λ[0] == 0};
d2sol = NDSolve[{eqns, conds}, {x, y, λ}, {t, 0, 100}]