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This question already has an answer here:

If I do an NDSolve of an IVP directly, everything works:

x[.5] /. NDSolve[{x[0] == 0, x'[t] == 1}, x, {t, 0, 1}][[1]]

But if I try to parametrise it, it doesn't

x[0][.5] /. ParametricNDSolve[{x[T] == 0, x'[t] == 1}, x, {t, T, T+1}, {T}][[1]]

I receive a ParametricNDSolve::ndsv: Cannot find starting value for the variable x. error. I cannot see what I'm doing wrong!? I guess this use of the parameter just isn't allowed?

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marked as duplicate by zhk, bjorne, Community Aug 4 '17 at 11:12

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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ParametricNDSolve is not helpful in such cases. However, you can use NDSolve with a SetDelay,

sol[T_] := NDSolve[{x[T] == 0, x'[t] == 1}, x, {t, T, T + 1}];

yfun = First[x /. sol[0]];

yfun[0.5]

0.5

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