Using Around with NDSolve

Question

I was trying to obtain the same result of a differential equation with to different methods the first one is based on DSolve and the second one is based on NDSolve

a = Around[1, 0.1];
b := DSolve[{y'[x] + y[x] == a, y[0] == a}, y[x], {x, 0, 1090}]
f[x_] = y[x] /. b[[1]];
f[2]

And with this code I get that $f[2]=1\pm 0.1018$.

Now I want to get the same result but using NDSolve:

soli = NDSolve[{p'[x] + p[x] == a, p[0] == a}, p[x], {x, 0, 1090}]
solie[x_] = p[x] /. soli[[1]];
solie[2]

But the Mathematica V.12 gives as result

NDSolve::ndinnt: Initial condition 1.00±0.10 is not a number or a rectangular array of numbers.

The problem is that I need to use NDSolve because I have a complicated differential equation (not the equation that appears in the example)

Answer 1

You can use ParametricNDSolve to analyse how sensitive the solution is to parameters or initial conditions. There are multiple examples on the reference page under "Scope".