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I'm trying to simulate a water tank. The dynamic of the system should be described by:

DSolve[{y'[x] == Piecewise[{{-Sqrt[y[x]], 0 < y[x]}}, 0.], y[0] == 10}, y[x], x]

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An infinite object ComplexInfinity might occur if you look at the -Sqrt[y[x]] term outside of 0 < y[x], however that branch should never be active under this condition.

enter image description here

So i don't under stand why Mathematica looks at those branches of the general solution where it is unable to compute the limit at the given points.

EDIT: Imposing the real number constraint gives the same solution as Daniel Huber however this solution stops when tank is empty. I want the solution to be Piecewise[{{1/4 (40 - 4 Sqrt[10] x + x^2), x < 2*Sqrt[10]}}, 0].

How can i convince Mathematica to solve this problem in a way that gives me a constant solution after the water ran out of tank?

( I'm running Mathematika 11.3 )

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1 Answer 1

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Remember, if not told otherwise, MMA assumes all variables to be complex. You have to specify that x is real and >=0:

DSolve[{y'[x] == Piecewise[{{-Sqrt[y[x]], 0 < y[x]}}, 0.], 
  y[0] == 10}, y[x], x, Assumptions -> {x >= 0}]

With this you get:

enter image description here

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  • $\begingroup$ This note about assuming complexity is helpful, however i would want a solution that has constant 0 after 2Sqrt[10] Mathematica seems to solve one branch and then not continue. The correct solution to the differential equation should be Piecewise[{{1/4 (40 - 4 Sqrt[10] x + x^2), x < 2*Sqrt[10]}}, 0] $\endgroup$
    – worldsmithhelper
    Commented Mar 16, 2021 at 14:29

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